Thanks for the suggestions, gents. I've been going back and forth on whether or not I should try to mount the engine with or without the transmission on. If I can get enough guys to help, I think I'll do it with the transmission in place. That's how I removed the engine from the frame, and it wasn't too bad (though I didn't care if I banged or scratched the frame at that time because it was so ratty). If I can't get much help, I'll do it with the transmission removed.
I had already considered protecting the frame, but I think I'm going to use pipe insulation instead of tape. I may have to use tape right where the engine mount studs go, but other than that, I'm going to line everything with pipe insulation like this:
I would think that would protect the frame pretty darn well.