Just another comment on the "P39 Q case":
P39 "in general" is a nice example at showing the concept of "favoureable" layout of the gun. Muzzle is very close to the propeller and the offset of its line of fire with respect to the propellel axis is small. Moreover the width of the propeller blade is small at its intersection with the line of fire. This minimizes the time the blade takes to cross the line of fire, thus helping to arrange a feasible solution for a four-bladed propeller.
On the other side, engine to propeller speed reduction gear is high. At least the one adopted in P39 Q. Other fighters featured lower reductions. Since, for the same engine speed, "the greater the speed reduction -> the lower triggering pulse frequency", the sawtooth drops at critical speeds are deeper and this effect is, in absolute values, greater for guns featuring higher free rates of fire.