Transfer Switch #4 checked out ok with the ohm meter, but when I installed it and tightened the wire connections, generator L2 had continuity whether the contactor was up or down. Interestingly, when I took it out, it check ok again. Something odd there.
Progressive sent me #5 after bench testing it first. Installed yesterday and everything looked good on the ohm meter. Fired up the generator with the circuit breaker ON for just one dedicated outlet. Voltages all correct. Also correct on the transfer switch itself. Check with A/C running as well. Looks good. Microwave still works too and the power converter seems to be ok despite the encounter with 90V for a few minutes when this all started.
Unfortunately there's no shore power at the storage lot so I'll have to bring it by the house to finish testing. But I'm confident enough that I closed up the basement.
Hopefully all will be well for a long time.