I figured this one out on my own.
The problem was that the Options field was not showing that I needed to select the type of file I was trying to import. The interface isn’t very good with this - you would think that by selecting a file type, EndNote would be smart enough to decide what it was and behave accordingly, or at least, throw up an error message telling you what to adjust if the import wasn’t successful. Nope, that’s not what happens, you need to see the Options button at the very bottom left of the dialog box, click on that, and THEN the options for importing come up.
Why is this not turned on by default? I wasted at least two hours trying to figure this out on my own, and the whole thing could have been avoided by a bit of better design. Hopefully the developers read this (optimistic of me, I’m sure) and can make an adjustment. Notwithstanding that, the program looks pretty powerful, and now that I know I can get my Papers 3 library into it, I’m looking forward to seeing what it can do.