A small update. I noticed that upon loading of the choose file/media/gallery window that the buttons on the file upload switch from two buttons saying "browse" and "upload" to a single button saying choose file. So I choose a file. Then it's as I said in my previous post.
I've tried manually uploading all of the files for the new version, since the first upgrade was a one-click from my host (DreamHost, in case it matters). My browser is current. Making the changes mentioned at http://trac.wordpress.org/changeset/7573 doesn't help (not even with clearing browser cache).
Since image uploads seem to be a problem for so many people, I've switched back to 2.3 for now. But the features of the new version look like they'll be awesome once they're all working. So if anyone has a fix you can share, I'm chompin' at the bit to make the switch back to 2.5.