Ok thanks for the tip, it’s good to know that I’m not the only one having this issue with the wheels rubbing each other.
Now, coming back to my problems, unfortunately adjusting the position of the snubber was not enough to prevent the tooth jumps. It’s a little bit better, but still far from the “0 tooth jump” of before the upgrade 
Here is a picture of my snubber. As you can see the gap is minimal, if not optimal. The belt is not in permanent contact with it.
Now, I don’t know how it was before. Maybe it was touching the belt… As the traces on the belt itself may suggest. If I look at the picture you posted above, I can probably try to reduce the gap even more, but I really wonder if this is the way to fix the problem.
I really feel depressed. I used to have a slow Strida that was working like a charm, now I have a fast Strida that cannot climb the smallest hill. 
Now on the other hand I realize that due to the change in the position on the bike I certainly can give less push with my foot when I start riding, thus needing more push on the pedal. But this cannot explain the whole problem.
Anyway, my last hope now is to find a way to adjust the belt tension. I’ll try to pass by a bike work shop over the week-end since I do not have the right tools. I’m a bit worried because it’s very unlikely that the shop will know exactly what to do, so I will have to tell them how to proceed… But even I am not sure ! Could you please confirm that 1.I first need to unscrew the big groove nut with the special key and the 2. then unscrew the nut that is right under the bike with a simple allen key ?
When I first tried I did not unscrew the big bolt screw before trying the one with the allen key. Is this the reason I could not manage to budge the last nut ?
Now, coming back to my rear break disc, and just for info, here is a picture of the calliper with the spacer (the white thing) I needed to add in order to re-center the disc into the gap.
For now the rear brake is working OK so I’m not going to touch anything.
Thank you all for reading, sorry for the pictures, taken with my crappy blackberry.