The Studer B-67, A-810, and Otari MTR-10/12 would all be good candidates for this purpose, and probably the Ampex ATR-100 as well. Any of these machines will treat the tape much more gently than the Uher ever will.
We have modified two of our machines to play at 1 7/8 IPS with good success.
I'm not sure what the issues are with getting the capstan servo to run at 15/16 IPS, but it is probably relatively simple, as the speed is changed by a series of logic divider chips.
You might want to contact John French at JRF and see if he can provide some specific recommendations. Their phone is 973-579-5773.