Hi again everyone!
I just wanted to give you an update! Captain Jack Sparrow's fins are growing back. He's still the ugliest betta on the planet, but he's just darling. He's a ravenous eater all the time, and he seems happy and healthy in spite of everything. The only real problem I've noticed (apart from the bad fins, which are definitely growing back) is that he gets nervous if approached from the side where he's missing an eye, obviously. So I just have to be careful when I reach in to clean him or anything.
The red floaty guy, who I decided to name Iago (I had just seen a performance of Shakespeare's "Othello," my favorite play, the evening I bought him. Iago is one of the greatest characters of all time!
) took a much longer time to come around. He was unexpectedly difficult to work with. Even with clean, warm water, he continued floating on his side most of the time. About a week after getting him and seeing no improvement, I tried Epsom salt baths and some daphnia when he became severely bloated. He's finally swimming upright and is able to move throughout the tank. He still doesn't seem hungry most of the time, but he eats occasionally. He just started to improve two days ago, so I'm still giving him time. But overall, both fish seem to be on the upswing.
Thank you very much to everyone who offered advice, assistance, and encouragement. It appears that my first rescue attempt has been successful!