UPDATE:
I followed the suggested paths of investigation only to find there is now no problem.
I disconnected shore power, took the cover off the transfer switch, verified no power on any 110 circuit and started the Generator. 20 seconds later, "ding": on comes the microwave. I verified the voltages and they were rock solid at 118.2 on both legs. I ran the AC units, shut down the system, and started the entire process again and have no issues.
The problem now is not knowing what went wrong and wondering when it will happen again.
Have ya'll seen this kind of problem as simply "one of those things", or is this indicative of a failing transfer switch or generator? The Generator has only 200 hours total time in operation.