ORIGINAL: LouW
Your analysis of the asymmetric thrust on a propeller when the airplane is in a climb is accurate. There is indeed a force acting on the propeller disc that tries to turn the nose to the left. That fact is not in question. The question is “how does that force manifest itself at the hub and how does the aircraft respond?” If you are not familiar with gyroscopes and a phenomenon called “precession”, I suggest you buy a toy gyroscope and study it some....
Not sure what you are getting at here. It's clear that P-factor is entirely different from gyroscopic precession, except that their forces are transmitted to the airplane through the propeller shaft.
I have done a bunch of aerobatics in Decathlons, and I found that if I pull up with at least 4.5 g loading at 140 mph or so, the precession generated approximately offsets the other left turning tendencies, minimizing rudder correction required to keep the heading, but only WHILE the airplane is changing pitch. That does not mean 4.5 g with another type of airplane will produce the same result. Once the airplane is flying again in a straight line, precession goes away. P-factor works any time the propeller is producing thrust AND the propeller shaft is not parallel to the flightpath. It is not a gyroscopic force, rather it is aerodynamically generated.