This question was posed at our retired engrs coffee shop group this AM
where such weighty issues are discussed ad nauseum.

The consensus was that probably minimum-engine prop dynamic structural
stresses (stresses other that the engine output torque and engine
output torque pulses - i. e. due to gryroscopically induced moments
applied to the crankshaft) will occur if the prop is vertical at the
point of maximum yaw velocity.

How that translates into a rough running system given the engine mount
system is not obvious.

I didn't personally experience the roughness of the original 172M that
had the improperly indexed prop, so I can't verify that the roughness
was first order as I originally stated. I just assumed it was.

At any rate, I still put my money on the prop orientation being
optimized to the second harmonic yaw motion of the engine.

The reaction and
rebound of a individual cylinder firing moving the crankcase.
I'm not sure but some of it maybe also be attributed to camshaft and
valve spring pressure. Valve train forces are much higher than you
might
first suspect.

The forces generated and reacted within the engine, stay within the
engine. They don't reflect outside. The whole problem of roughness
however, has to be considered with the possibility that the prop or
engine has a first order out-of-balance that is dominating any
observer's attention.