Spiraling slip stream is only one of the propeller effects that right thrust can help. The larger reason for right thrust is P-factor at slow speed. If the prop disk is not exactly perpendicular to the air stream, the blades will see different AOA on opposite sides of the disk. This shows up the most during slow flight. Nose high attitude tilts the prop arc back causing the descending blade (on the right) to take a bigger bite out of the air, and the rising blade (on the left) to take a smaller bite. Basically offsets the center of thrust to the right causing a yaw to the left.
Your description of the aerodynamic forces is correct. And your explanation of left turning tendencies is seen in many books, however it simply isn’t true. The problem is that the rotating propeller is a
gyroscope rather than a stationary surface. A force applied to the rim of a gyroscope
always appears as a reaction displaced ninety degrees to the applied force. Thus the left turning force applied by aerodynamic force on the propeller disc produces a
pitching moment at the hub. P-factor is real but gives a pitching moment not a yawing moment on the airplane. The left turning tendency of many airplanes when operating at slow speeds and at a high pitch angle is due to propeller swirl, period. Arranging side area can reduce or eliminate this if desired.