The project is still alive - ordered the 3 12mm shafts to be made at an engineering shop.
Will be a little bit expensive as they are using the good, hardened stuff and have to add a finishing touch to the cog.
I made a little drawing for the order I'd like to share.

This had to wait until I was finished making all those blanking plates to keep the oil in the transmission - time consuming and tedious, especially as I want it done "right". I estimate an effort of 80-100 hours going in the transmission after it was pulled apart:
- cutting it open
- fabricating the motor mounting plate
- blanking and cover plates, and all those grooves
In retrospect, I would advise using a transmission that's sealed more easily like shaft drive or 2-stroke.
I will have more updates soon.