This is Samuel again... 48 hours after initially experiencing the problem I originally posted. More facts:
1) One of the air conditioners runs normally using either generator or shore power; the other one appears to exhibit the original issue of starting, surging, and shutting down, with this exception: when on shore power, the A/C shuts down, but the rest of the RV maintains power.
2) The shore power has a surge protector installed. One leg of the surge protector has been "blown" -- I have returned it for replacement.
A question: is the Power Control panel the same as the Power Transfer panel?
If not, please clarify what it is, and suggestions about diagnosing any issues with that panel.