Dear Blackstridaaustria,
Thank you very much for your detailed answer.
You are right about the rear disc: I have mounted it in the wrong direction. Congrats for catching this detail on the pictures ! 
Unfortunately for the time being I don’t have the time to disassemble everything to put it in the right direction. I don’t know if it makes any difference, because to me it looks like a perfectly symetrical flat piece of metal, but at the same time it could maybe explain why I had to introduce some spacers (about .5 mm) to recenter the disc into the brake shoe. And if there is a drawing of an arrow on it, there must be a reason !
Now; talking about the snubber, I’m pretty confident this was the cause of the tooth jumps. I checked and it was completely loose, so basically it was like riding the Strida with NO snubber. Tonight I fixed the thing, and tomorrow I will see if this simple change will solve the problem.
For the belt tension I used (and ruined) Allen keys, not screwdrivers, sorry for the misleading message. Anyway I really could not unscrew the big groove nut. I’m glad to see the picture, it looks like you need some special tools if you really want to do it in the best conditions. If the snubber fix is not enough to stop my belt from slipping, I’ll probably try to find a Strida reseller to have it adjust the belt tension for me.
All in all I’m still happy with my upgrade, the gain in term of speed is noticeable and really cool.
One last thing however: now when the bike is folded the two mud guards have the tendency to tangle up, and sometimes the two wheels will rub one against the other with a squeaking noise… Not a big issue, but it’s annoying.
Thanks for your help.