I attempted a demo import despite the 404 errors, but the only option available was “Import WP Options” checkbox. All others were missing. The process stalled during import with no import status indicators. I abandoned the import screen and no data (pages, posts, etc) was imported.
Client doesn’t want to provide me with support pin to troubleshoot, so I’ll let them know it’s a file permissions issue specific to WPEngine I guess. 🤷♂️