I FOUND A WAY TO FIX 803-3001 WITHOUT LOSING YOUR BOOKMARK*
I was just about to start a new summon session when it killed itself on me again. That meant I was gonna lose 5 orbs AND have to wait until I had 4 more orbs to start over, so I wasn't putting up with it, and I figured out a way to get around losing your bookmark.
DO NOT DELETE DEVICEACCOUNT.XML! Put it somewhere safe for using it later.
Start up FEHeroes and link your account again like usual, I went ahead and accepted the terms of service after the reset for safety.
Exit the game and open up the new deviceaccount.xml, and replace the "sessiontoken" string with the one from the original deviceaccount.xml that you made sure NOT TO DELETE.
Voila! Tres bien! You can reload your bookmark AND make use of the stamina/orbs/arena swords/light's blessings that you almost wasted on the error!
It was a real lifesafer, too, because right when I got back, I got a 5-star Jaffar and Merric from my summon session. I never thought I would get away with it, but I did! AND YOU CAN TOO!
*Update: I could not replicate the fix after I got the error again, just at the end of a fight this time (in particular, a training tower map). Perhaps it doesn't work for battle bookmarks? I am wondering if maybe there are different "types" of "bookmarks" that the game can continue from; next time I get pulled from the middle of summoning, I might need to see if it asks to delete the bookmark "from another device" or if it works differently. I'm going to keep trying to see which situations allow for the fix and which don't. What I know for sure is that the "deviceAccount" and/or "devicePassword" strings from the previous deviceaccount.xml will cause the 803-3001. If I can get any response about toying with deviceaccount.xml, it might help.