Okay, so would it be even remotely possible to make a mod that would organize saves by character at the loading screen? Can I read save files with papyrus? Can I even mod the main menu beyond replacing image or music files?

As far as I know, at the moment, No, No and No.

There is a Menu-Mod being worked on, I believe ... search on this forum for some details. But I don't know if that will include functionality to let you play with the Saved-Games bit (it's intended for the in-game panels, I think)?

Papyrus reading saved games ... Not really. You can get at assets in one mod, from another mod, but I don't think that is what you mean?

To my knowledge, this can't be done within the game. The logic that orders the saves in the menu is probably buried in the source code and not something accessible in the .swf.

The only alternative would be to create an external utility that would read save games and make appropriate hex edits to save games based on character.

Papyrus cannot "see" save games in any way. Papyrus cannot access the PC's directory structure for the most part. A savegame is just a snapshot of the current session that your papyrus scripts occupy at that time.