especially considering the pitch moment they exert. Seems to me that the yaw would be more evident than the pitch
Couple of additional things to consider. Especially at very low speed, high alpha, and with a fistful of thrust (did someone mention the miss from the flare ?) we can get two additional sources of unwanted excitement and which can impact adversely on pitch and yaw stability.
First, on props, the P-factor moves the net prop thrust position laterally. If this be outboard, it can worsen yawing considerations, whether singles or multis. Indeed, in a big, hairy, multi-thousand HP military bird with one motor, one could find a situation not unlike Vmc in a multi.
Second (props/jets), the high alpha results in a significant turning of the incoming airflow either into the prop disc or the jet's nacelle. Just like with a wing, this change in direction provides a change in momentum which gives you a vertical force (lift). In the case of the engine, this vertical force might be well out in front of the wing and provide a significant nose up pitching moment. Generally referred to as the prop/nacelle normal force. For piston to turboprop conversions, where the engine is pushed out further for static CG considerations, the effect can be sufficient that the pitch characteristics in the miss become unstable and the aircraft needs a SAS mod to fool the pilot into thinking things are still stable.
Obviously, if we consider slipping/skidding airflow, the pitch problem can become a yaw problem.
some of the yaw we experienced in that little jet ( A-37) might well have been gyroscopic precession
Sure could but consider the nacelle normal force as another option ?
most of us concluded that it was the awesome increase in thrust from the original design
Very relevant - consider piston to propjet conversions and jet engine growth. I suspect that some of the MAX's problem was associated with nacelle lip lift.
This is a very ambiguous question.
The joys of pilot theory training ....
It is why I rehearsed bad situations
.. and why many, who didn't, are no longer here to be able to offer thoughts on this and that.