I should have been more polite in my answer.
The difference in blade angle is rather small (+/- 0.5 degrees at a 10 degree angle of attack). 2/3s of the effect in the example I worked is from the different velocity of air over the climbing and descending parts of the blade. Once you are into the takeoff roll (probably less than 50% of Vso) most props appear to function close to the idealised model (i.e. they are not partially stalled and are operating at some reasonably large fraction of their design efficiency).
Static thrust is quite heavily influenced by disk diameter, hence, your observations
I would have thought P-effect is negligible in the takeoff roll (and certainly has nothing to do with the sudden left turn at the start of the roll!), measurable in a Vx climb, minimal in a Vy climb and quite significant in slow flight. I have never seen a sensible argument for why the torque resulting from the slipstream effect would change materially with angle of attack or the relatively modest speed difference from Vy to Vso - so measuring the rudder deflection over that speed range (and the angle of attack required for unaccelerated flight) you could determine the P-effect (as it seems the only effect dependent on AoA).