The Sidewinder motors are RS-550 models, with 3.2mm diameter shafts. Note that the fit into the pinion gear is VERY tight, so be sure to line up the vise or press before you start pressing the shaft into the gear. Otherwise, you’ll need to buy another Sidewinder like I did [don’t tell my wife!]; once bent, those shafts are nearly impossible to straighten again.
As for the ideal gear ratio, I wish I had a good answer, but don’t. I measured the force produced by my rig using a digital kitchen scale, but that was a couple of years ago and my aging brain has completely forgotten the answer. But if you spend a few minutes reviewing gear theory, and measure the force produced by the Sidewinder gears alone (again, with a digital kitchen scale), AND factor out the mechanical advantage provided by my pulleys, you should be able to calculate the gear ratio needed to obtain your target forces. One possible set of targets are those produced by the 1100-euro Brunner FFB yoke - namely 40N on the pitch axis and 1.7N-m torque on the bank axis. There may be some technical reason why you cannot achieve those same forces by choosing the right gearbox ratio, but I don’t know what those constraints are. (My dad and my grandfather were both engineers, and if either of them was still alive I’d ask him, but it’s too late for that.) In any case, I would suggest using AT LEAST the 11:1 gear ratio.
I would offer more specific suggestions, but I’m on a plane right now (the first in two years), and at the outset of a vacation(ditto). I’ll try to update when I get back in a couple of weeks. Until then, I am not optimistic about my chances of surviving my wife’s reaction to me telling her that I had brought this topic with me on the trip she spent so much time planning. 8-[