Probably not the case as you have multiple bikes, but thought I'd point out that sometimes your frame or fork alignment could be a little off. I believe my very first steel Trek road bike had this issue, although it rode beautifully, I was never able to ride that bike no-handed, use to frustrate the heck out of me, when I would see guys sitting up no hands at the end of a long ride! Every bike I've had since then I can ride no handed no problem.

Which brings up another point, a couple months ago I sat up during a ride and my bike would track off to one side or another and felt really unstable. When I got home and was trying to figure out what was going on, I realized my headset bearings were shot and had started to 'index' on me. Had the headset replaced and one again rides beautifully no-handed. Check your headset and make sure it feels smooth and isn't slipping into grooves in it's range of motion.

Wanted to point out those two things from a mechanical perspective so see if it's either of those.