The door doesn't appear to be the problem. All looks right in both photos. If this wasn't working properly, the counter wouldn't move and winding would never stop.
There are a couple of levers that travel from the lens board into the wind side of the camera. I bet that by moving the lens board back and forth you jiggle something inside the wind mechanism into its proper position, activate a linkage, or some such change.
All in all, sounds like a dirty wind mechanism needing a good cleaning. Possibly a couple of interlocks adjusted.
Service manual- https://docs.google.com/viewer?a=v&q...F1WmbOAdnACKFw
The best Autocord repair guy I know is Karl Bryan in Oregon, USA. Along with lots of experience and skill, he's also a helpful man. Send him a note and see what he thinks? If you have him do the work and mailing works out, he'll be quick and thorough. firstname.lastname@example.org