Hagglunds, a swedish hydraulic motor manufacturer, seems to be the type of motor you describe, but you seem to be trying to match the winder to the motor rather than the motor to the winder requirements.
Establish the winder requirements first tnen select a motor to suit. You may find you...
Is this machine a devlopment project or is it to be a production machine.
If it is the latter, you will need something considerably more precise than a controlled speed system.
I would propose a pair of capstans with buttons to engage the holes in the webs, one for each web, driven by a pair...
Not necassarily a simple problem.
If the device involves a steel bearing in a steel housing, and the differential expansion is transient, i.e during warm up, then you will need to look at the source of heat and determine relative rate of heat transfer and consequent expansion rates...