Hi, thanks for documenting the gearbox rebuild. Very interesting!
I notice in your final picture that you have new gear position sensors
No new sensors. Not sure how hands on you want to be, but with VCDS or what I have been using OBD11 you can go pretty far in diagnosing. You can see all the adaptation settings and see if they are in range. You also can have the trans 're-lean' shift points. (be careful as if it does not like this, you can be stranded).
I tried the latter for my issue and car would not go into gear after. I unhooked batter, and let sit for a while and reconnected and got it to go into gear. (trans error still showing). I tried "Basic setting #2" again, and it did the same thing again.
I then took to Audi for diagnostic and they confirmed that it was likely the 3rd gear fork and possibly synchro.
I am going to try to get it shipped off tomorrow.
Sorry I dont have any more answers.