IMO the biggest flaw with Awakening is the story. It has easily the weakest story of all the Fire Emblem games I've ever played, and I think the overcomplicated, Final Fantasy-esque plot devices play a big part in that. Most the other games had relatively simple worlds, setups, and plot devices that just utilized a lot of political intrigue and some plot twists to make an engaging story. Awakening just fell pretty flat in that regard.
But, not done that can be done to fix that without completely rewriting the game's script. I like the OP's idea of a FE4-esque time skip, but in general, I think there are so many possibilities on how to change the story that it would be impractical to discuss.
Son instead, here are my three easy steps to making this game passable on the mechanical level:
1.) Eliminate Grinding
I agree with the OP as to the principle, but not so much the execution. As much as I love Sacred Stones, I feel like it set some subpar standards for the series, among them the ability to grind which is fueled by the ability to free-roam on the map. An easy solution to the grinding problem is to disallow free-roaming on the map until the postgame. This would also help add an actual sense of urgency to the game's story that it's sorely lacking. (The ability to take a leisurely vacation to Valm while the plot wants your army to rush to the Dragon's Table as fast as possible is at least part of the reason why the game's story has little impact, IMO.)
2.) Balanced Higher Difficulties
I pretty much agree with the OP on this one. I enjoy a good challenge meself; I love me some challenging-but-fair Megamanz, but I'm not touching Awakening's Lunatic mode. No bragging rights are worth that kind of misery.
3.) Fixing the Magic System
This was by far the simplest / most obvious to fix thing about the game. Why, when not so long ago we had the lovely elaborate double-triangle magic system from Radiant Dawn do we now go to just having Wind and Dark magic? Yeah, Fire and Lightning are in the game, but they're pointless since nothing is weak to them. That seems pretty unbalanced to me, and makes me wonder why they're even there at all if the Anima weakness triangle doesn't exist. That, and the fact that any magic-user can use any type of magic really lessens the impact of the different elements of magic even more. RD had a great system, why fix what isn't broken? (hell I don't even care that Light magic isn't in the game; it'd be nice, but most of the classes seem like they were designed without it in mind, so meh)
Easily fixed by doing this:
- Mages > specialized Fire / Wind / Thunder Mages
- Dark Mages / Sorcerers use only Dark Magic
- Sages use all three + staves, making them the only class to get all three
- Fire Mages upgrade to Sage or Dark Knight (Dark Knights wield Swords and Fire Magic)
- Thunder Mages upgrade to Sage or Valkyrie (Valks use Staves and Thunder Magic)
- Wind Mages upgrade to Sage or Darkflier (DF use Lance and Wind Magic)
- Tactician picks a type of magic to specialize in, then another one on promotion to Grandmaster for a total of Sword + 2 types of anima
- Beast units weak to Fire / Wyvern units weak to Thunder
(also have Pegasus Knights be only Flying / Wyvern Riders be only Wyvern; Griffon Riders being both Beast and Flying would be more unique that way)
It sounds more complicated than it actually is, but yeah. That's what I'd have done.
EDIT:
I'd just like to say in response to this that time constraints absolutely are an issue in this field. I don't know the details of it myself, but everything has deadlines in the professional field, and you just have to work with what time you have.
Incidentally, while I regret that nearly all the effort in Awakening's script went into its very high-school-locker-room-esque supports, I think it's at least noteworthy to realize that this opens up the Fire Emblem series to a larger audience, meaning not only the survival of the series (it wasn't going to continue after Awakening if it didn't do well), but the possibility of greater improvements now that it's sort of hit the 'mainstream' among gamers. It may not have been as great as previous games, but at least there's that silver lining.