Here is a polar for a piston single-engine aircraft:
(This is lifted from a Russian manual for Yak-52, so $C_x$ is drag, $C_D$, and $C_y$ is lift, $C_L$).
1 is the 'normal' case without propwash. 2 is nominal, and 3 is the max takeoff power.
It is evident that the whole lift curve slope $C_L^{\alpha}$ is increased significantly (by some 30%) as the engine revs up, with $C_{L_{max}}$ reaching 2.
But what immediately follows, amongst other things, is that the AoA (pitch) stability should increase accordingly: it is proportional to $C_L^{\alpha}$ (as well as to the distance from NP to CG).
However, somehow I've never seen this fact mentioned explicitly, despite it being quite significant. Can anyone confirm it, either from literature of experience flying higher-powered prop aircraft?
(It may not be very obvious to feel the difference because other conditions are rarely the same between idle and full power, but the closest approximation I can think of is glide descent vs full power climb at the same speed: the aircraft should be 'stiffer' and possibly more oscillatory in pitch at full power. However, propwash over tail may mask this effect; perhaps a twin is a better testbed for this...)