Oh geez, I figured it out. Sorry to have wasted all your time, but hopefully someone else will be helped by this post
Turns out, when I download, I have to click "open" instead of save. If I do save, I have to import it into ADE, and it won't copy over into my reader. If I hit "open" it opens directly into ADE (like my library books) and I can copy it over into my reader.
Is there any "DOH!" award on this site? I think I might seriously be in the running....