It does sound that way Deejay. Because the self-aligning bearing at the sprocket end acts as a non-driving universal joint, the cutter shaft is effectively like a car-type propeller shaft, and misalignment of the two ends (within reason) will not induce stresses in the PTO or the rails. So, alignment errors seem to be off the agenda. I'd still like to know whether the Briggs engines vibrate more than other engines though. One factor that might be relevant is that the engine-mounted-on-the-frame-rails might have a resonant frequency within the engine's operating speed range. While all of the relevant engines (Kirby Lauson, and Briggs 8 or 9 cubic inch) should, and probably do, have fairly similar unbalanced forces (see post on half-balancing in another thread) but different engine weights, the resonant frequency will vary from engine to engine. Resonant frequency is a function of spring stiffness and the mass of the vibrating object. The Kirby Lauson is probably rather heavier than the Briggs, so conceivably the Kirby Lauson has no resonant frequency within the common operating range, but the Briggs does. Measuring the amplitude of mechanical vibrations is feasible without special equipment, if anyone wants to do it.
Barely relevant story: I once found an engine speed at which the throttle return spring resonated in a fairly popular car. (You could feel the vibration through the accelerator pedal.) To find out whether it mattered, I made a point of driving the (new) car at that engine speed on the freeway on the way home from work, and on the way to work the next morning. The spring broke on the second day. I had it replaced and broke the replacement in another two days. Then I stopped doing it. Driving on a freeway at peak hour with no throttle return spring isn't fun after the first couple of times you do it. It wasn't dangerous (there was a rather light secondary spring in the system, as there usually is on car throttles) but there have to be limits to what you do in heavy traffic.