Given that these things are mouse power rather than horse power how practical would it be to rig up simple direct drive stepper motor system?
Generic motor and "twiddle a knob speed control" drive from the usual affordable sources. Simple fork drive on the end of the motor shaft. Motor mount arranged so it can slide sideways to engage and disengage the drive.
Obviously a belt drive speed reduction set up with sliding fork clutch would let a smaller motor be used and the speed reduction would probably give a more controllable drive but it needs more parts and more making. With a belt drive a DC motor would be fine too so probably a bit less costly.
That said were I to do the job I'd use a pair of nylon gears with the motor on a swinging pivot mount, like a car alternator, to engage and disengage the drive. Large gear living on the leadscrew shaft, small gear on the motor. Choose gear sizes to fit and give a sensible speed. Motor with speed control can be stepper or DC to choice, taste, price or lucky find.
I'm not in love with the standard direct drive from the spindle idea which doesn't allow the feed drive to be engaged or disengaged when the spindle is already running. But, as ever in the real world, its a question of how much performance and design elegance the customer can afford. Generally much to be said for "Cheap'n works … but…!" so long as the …but… isn't too obtrusive.
Clive