Sorry to hear of your drama. Not plesant having a trip end abruptly that way.
This particular scneario is one on me. I don't recall anyone posting anything similar in the last couple of years. At least nothing so dramatic.
I see looking at the specs for the Access the Onan generator is rated at 4000 watts which about 35 amps capacity. If the microwave was actually running at the time plus TV, fridge and a few 12v lights off the inverter I'd guesss you were drawing around 30 amps. If the microwave was idle then it'd be only 15 amps or so. Either way the system should have been able to handle the load.
Glad it was handled for you. Man, that had to be a pricy warranty repair. Make sure you turn on EVERYTHING electrical at least once before you leave. If it fried the converter there could have been a power surge just before it went. Turn and use all radios, all functions, all video switches, anything that uses power.
If something is not working or acting right, it's better to know sooner than later.