This is a bit random, but everything was working fine until I activated ‘The Grid’ plugin. Now the importer goes through the motions, but only returns the first event I chose, doesn’t acknowledge that it has already imported it, and brings in an image file format that the media gallery can’t render.
Anyway, just chucking this out there in case it just might trigger some strange fix, or in case anyone else ends up with this problem. For now, I’ll just not use The Grid plugin, which is a pain, but not as much a pain as this plugin not working!