Looking at the process more today, I think we can simplify by orders of magnitude.

Steppers stop better than they start, especially with a load on them - I am fairly confident that we can get away with just a ramp up and run signal, no ramp down so its just ramp-up, run, stop. Don't forget - this is not CNC, an accuracy of a few mm's is fine here.

This means we can possibly look at a simple circuit based on a 555 ic with a few components to give the ramp and adjustable speed, i have seen something like that on the 'net, will try and find it again.

That, with a suitable drive and PSU will be it, nothing more needed apart from a run / stop trigger.