Or like, a small case with a glass door, so you could still have them on display? Or would sealing them up like that just make the mildew problem worse?

Sorry you have to deal with that. Mold sucks when you're collecting stuff. I remember having to pop the heads off of my My Little Ponies and boil them to try and kill mold so it wouldn't spread to the rest of my collection. Never accomplished anything but to make my ponies look like shit. And books are a million times more fragile. Other than freezing, I can't think of any way to treat a book for mildew that wouldn't ruin it. Maybe letting it air out for a long time in a dry location away from your other books?