Hi, and thanks for all the advice, and the terminology info. I didn't know you could grt square threaded rod! I hope we can keep MI5 out of this.
Enc is a pic of what I have in mind. It's supposed to be a compact puller. The two gears at the left cause the leadscrews to turn in opposite directions at slightly different rates, in turn causing the pinion to move along, slowly but powerfully.
I've drawn triangular teeth because it's easier, but square would be better. Steel, probably. If necessary, there could be pinions above and below the one shown, to help stop the screws bending.
In the end, I'd like to make it even more compact – 1/4 the size shown, if that turns out to be possible.
Btw, I just mentioned the woodworking lathe. I don't think it will be of much use for this 
Thanks again,