I wouldn't mind said 5th route. Though I wouldn't call it a "Golden Route" so to say. I wouldn't even call it a "Revelations". I don't mind the fact that it wasn't made, but I certainly wouldn't have minded the fact if it was.
If I had to give my two cents on how to execute said 5th route, I'd personally do it this way (Though please note that the only route I haven't done is Silver Snow, so if there is a large piece of information I am missing that throws this out the window, please disregard my statements here, and please do let me know that I should play Silver Snow before trying to make some idea that really isn't going to matter. Also I'm sorry if all of this seems scattered, choppy, etc. Also obligatory SPOILER WARNING):
At least two other routes must have been completed (with a few changes here and there, will explain later)
Sothis knows exactly who she is. No amnesia, nothing of the sort. Byleth has been this sort of "silent, expressionless" person all their life due to Sothis being in their head. This is due to the fact that They consider Sothis a friend (and she does them), and so therefore, Byleth doesn't see the point of talking most, if not all, of the time due to traveling around with a mercenary band all their life. I would say the "expressionless" part is mostly due to Byleth expressing emotions in their head with Sothis, and because they are doing so inside their head to someone else, their body doesn't feel the need to do it physically.
However, I will say that because of the way Sothis technically died, she is exhausted and most of her power is sealed, which explains the limited divine pulse and the constant napping (although Sothis doesn't need to be a sleepyhead). Through Byleth's 20ish years of life, Sothis would slowly tell them about her previous life, talking about Rhea, the constant experiments that she did, the Red Canyon, etc.
So when Byleth meets Dmitri, Claude, and Edelguard for the first time, Byleth sort of knows what's going on (in the first few chapters of the story, but the player does not. This is to establish that WE are not Byleth, and that Byleth is some type of unreliable narrator. I personally don't like the avatar system to an extent. I think having a customizable character is a great idea, but to have US the player as that character? No thank you. Which is why I would propose that even though we can still customize Byleth to an extent, WE are not Byleth, and when we make choices for Byleth, it is Byleth thinking about what they can say, not to give US the player a choice).
First, a few small changes (technically huge ones) to Crimson Flower: Rhea is more mentally unstable, and any options to spare students are not there (this particular change is for all three routes, and under the assumption that you cannot recruit students from other houses). When Rhea dies, the crest stone inside Byleth does not break.
After Byleth sees the destruction of at least one route, they resolve to refuse to let this war happen, and Sothis pushes her power to the limit to divine pulse back to the beginning of the game, so that Byleth has another chance at trying to stop this war. For the "5th route" (yay, i'm finally talking about it), Byleth or Sothis (through Byleth) would propose to Rhea and Seteth, that instead of the three of them teaching the three houses separately, they each collaborate to teach all three houses at once. Byleth would support this idea with the fact that it might make stronger diplomatic relations among the students, so that the "unstable peace" can become more stable. No one wants a war breaking out, and if the future leaders of Fodlan were friends in what is essentially high school, than the start of a war would be less likely, as logic might dictate.
Rhea, intrigued by a new idea, would most likely support this. Seteth might be a littler cautious about it. Thus the three classrooms become a single, large lecture hall (or something like that).
So, the issue of Sothis not telling Byleth to let Rhea know that she, Sothis, is alive. I would say that Sothis disapproves of what Rhea is doing, and what she's done, and so Sothis is angry enough to just not say anything to Rhea. Sothis would also say that doing so might result in Byleth (at least in heart and soul) might be killed due to Rhea wanting her mother back, not some random stranger AND her mother.
The player would then go through the game as Byleth, with Sothis, raising support with all three lords, and trying to raise support between the students from different houses. Due to Byleth's prior knowledge of each student, they would be more successful in doing so.
I would say this also unlocks a "group support" between the three lords and Byleth, in which all 4 of them are present and are talking. Each support would be story locked. I would say the C support would be obtainable after the Lonato chapter, in which Byleth and the three lords talk about the church, and begin to talk about crests. it would essentially show Byleth the problem of how close minded the three lords are to one another, albiet how similar their ideas are. After the Miklan chapter, the C+ support would be obtainable. This is when Byleth openly discusses crests, and would ask that all three write some type of essay on their views (This essay would probably be given as a whole class assignment). Due to this being after Miklan, Byleth would have heard part of their views after the raid on the tower. All three lords believe that crests, in some way, shape, or form (from what I've seen), should not be the center of the universe. Byleth, after reading these essays in silent, would call all three lords and say something along the lines of "these essays are all the same."
Byleth would explain how uncanny it is that all three lords wrote similar essays, and would ask (as it is their job) if they collaborated. When the lords deny it, Byleth would say something similar to "Then perhaps the three of you should talk more. You all have similar ideas, perhaps the future leaders of Fodlan will be able to lead us to a more prosperous future", indicating to the lords that the three of them might share the same goals.
The B support would be obtainable after the Remire village chapter (where you fight Solon and meet the flame emperor for the first time). However, one small change: Byleth would confront the Flame emperor alone, without Jeralt. The Flame Emperor would do his thing, asking Byleth to join him, and claim that they didn't order this attack. Byleth would immediately up and say something similar to "Listen, Edelgard. Regardless of whether you did or not, you have given me no evidence?" The FE would obviously be shocked at this statement, and Byleth would continue. "There's no reason to start a war over crests. The others are coming. Go." and the FE would flee in a panic when they see Jeralt + the other Lords coming.
The B support would contain the lords and Byleth talking about the Flame Emperor. Dmitri would say its unforgivable that innocents were harmed, Claude would agree. Byleth would play devil's advocate and say the FE stated that he didn't do it. Dmitri would obviously get angry over this, and Byleth would talk about how some subordinates or allies do what they want without the approval of others. Claude would be shocked, but would eventually agree that its a possibility that the FE's minions are so devout, that they might go against their leader's wishes to help their leader in the long run, and so that wouldn't be the fault of the leader, though the leader would have to take responsibility. Dmitri would reluctantly agree that the culprits should be caught, and if it is proven that the FE didn't have a hand in the Remire Village incident, he would calm down. Edelgard would be silent this whole time, and Claude would touch on this with some type of remark. Edelgard would then excuse herself, thus ending the support.
The B+ support would be obtainable after the death of Jeralt. It would start by Edelgard coming to Byleth, apologizing for his death, saying that it wasn't supposed to happen. Dmitri and Claude would then enter, with Claude making a remark about how Edelgard is acting like she stabbed Jeralt herself, or ordered it. The conversation would then spiral to what the FE wants. Claude would say that it has to be something against the church, as it's the only thing that makes sense, but the reason is unknown. "if only there was a way to talk things through". Dmitri could then bring up the fact that Lady Rhea isn't "clean" herself, stating that the execution of the western church members make her no different than that of Solon and Kronya. Claude would be shocked at this and ask Dmitri to quiet down, as they might be heard by a knight of Seiros. Edelgard would then say something along the lines of "but doesn't that itself prove the point that something is wrong with the Church? They stop conversations like this and restrict certain knowledge from ever reaching the ears of the people". The three lords would talk about this a little bit more but than agree as a whole to investigate the church more.
Afterwards, Edelgard would write down her knowledge of the churches shortcomings and try and pass it on as a tome she found. She would also try and get TWSITD off her back, saying that there is no reason to work together anymore, since she sees that with the help of Byleth and the other two lords, taking down the church might be possible.
In the A- support, which would be available after Byleth merges with Sothis, Edelgard would reveal her "findings" to the other three. Claude and Dmitri would be obviously surprised, while Byleth would reveal why their appearance changed---Sothis, the experiments of Rhea, how Rhea created the three factions. They would not mention anything about the divine pulse, as time travel might...cause some problems. Edelgard still has no way of knowing how Byleth knew she was the FE, but she can chalk it up the "oh, god powers".
After that, that is where most of the game would change. essentially, Byleth would have the three lords and some troops follow them and Rhea to the Holy tomb, and confront Rhea with the evidence that they have. Rhea, would most likely be both enraged and happy (because her mother was alive, enraged at the audacity of them, and the fact that Byleth isn't her mother). However, before she can do anything, TWSITD attack, trying to steal the crest stones. After the fight, they would learn of a huge army coming to attack the Monastery. Big fight, monastery in ruins, At the end, Rhea is assaulted by TWSITD, forcing her to reveal her draconic form. Byleth tries to save her ---> timeskip.
After Byleth wakes up, they find that TWSITD have taken over Fodlan, the Adestrian Empire and Holy Kingdom are putting up a feeble resistance, and the Alliance is in inner turmoil as TWSITD is using the Gloucestor family to try and undermine Claude. Rhea is nowhere to be found. Byleth enters the ruined monastery to find what remains of the Knights of seiros, distraught over the loss of Rhea. Byleth rallies them together, stating that the evil that is TWSITD must be purged, as they caused all this death and destruction. The timeskip would essentially be the player going all over Fodlan to defeat TWSITD, gathering former students and eventually recovering Rhea's battered body in Shambhala.
The A support would be after all three lords are saved by Byleth, and they all vow to make Fodlan a peaceful place. Rhea would step down from her position as Archbishop, but state that the common people still need someone to look up to. The three lords agree to some extent, each with their own problems, But Byleth vows to make sure the church doesn't go down the wrong path. With the new Dawn of Fodlan near, they begin preparations to fix the problems that have been plaguing Fodlan: isolation, racism, crests, etc. That's when the final battle starts, and they fight a resurrected nemesis, the ten elites, etc.
The epilogue would show how the Church would become a smaller figure in the governing of Fodlan, while the three lords unify Fodlan over the years, and eventually make Fodlan a much more prosperous place.
Wow. That was really long.