Great !
So, with the lower acceleration, the error does not appear, yes ?
Now, to confirm, put it back up to 100 again, and see if it now appears.

If it does, with high confidence, you have encountered the problem.

To quickly localise the max practical acceleration, first make sure you can reliably repeat the problem.
Then split the difference-
3-4 tests should get you very very close to the optimum number.

Ie, if at 100 it fails, and at 10 it does not (diff 90);
Try 10+45 = 55.
Errors, try 10+45/2 = 32.
No error, try 55+45/2 = 77.

And so on..

If you want more acceleration and better results, use HTD pulleys, 5 mm profile, 15 mm wide, at 1:3.
16 teeth small pulley, 48 teeth big one (less than 16 does not have enough belt wrap).
This will likely work reliably at around 100 (or could be even more) as you now have 300% more torque available.

Best,
h-

I did the tests a few times and the z-axis comes back to the correct zero position. This is after I have reduced the acceleration.

-- 

-hanermo (cnc designs)