Well, very strangely, I sort of got it to work.
FOR MAC/OSX:
1) Open up a Terminal window
2) Type gzip and then drag the XML file to that line (or type in the location manually) - hit enter.
3) Use your new .gz archive when selecting XML import file.
4) You're done!
FOR WINDOWS
- Use 7zip to create the .gz archive
Not sure WHY that worked, but it did. I could assign posts to a new user, and though the files were deleted from my old server, at least it checked for them. Pages and posts all look good!
I'm not marking this as solved, because it still doesn't tackle the underlying issue. I would love to hear anyone's additional thoughts.