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. A force applied to the rim always results in a movement at the hub ninety degrees out of phase with the applied force. The force on the propeller disc tending to turn the nose to the left affects the airplane as a nose up pitching moment. If the propeller is rotating it can’t react any other way.

As to propeller swirl, I would be the first to admit that the illustration in “Stick and Rudder” is misleading. The swirl (or more appropriately twist) is, of course, only on the order of a few degrees at the most. My airplane is a Piper Cherokee and has rudder trim. If I trim the rudder to eliminate any left turn in a steep high power climb it only takes two or three degrees of deflection. This is about what one would expect from propeller swirl alone. There is no need to add the infamous P-factor.