I did it! After a lot of reiterations that flimsy belt drive is gone.
I printed before measuring, I ran out of filament at 97% og the print and I designed stuff that turned out to be stupid.
I also got rid of those small blocks to hold the belt axle and made new components combining adjacent parts to one sturdy piece.
The gears are a litte inaccurate but running it for a few moments helped out a lot grinding down the inaccuracies from the printing and I suspect they'll be a lot smoother after some more running time.
Check out the video(I deeply apologize for filming in vertical mode)