Had some more time to mess with this today.
Here's an update on the symptoms.

Gas genset, 7Kw Westerbeke 1998. Looks like the carb has probably been
off (no red paint). Other than that, no visibile repairs/replacements.

To start this unit, you push a button that instead of preheat on a
diesel unit, it bypasses the low oil shutdown, it runs the fuel lift
pump, and
energizes a choke solenoid that closes the butterfly in the carb.

What I first found was that the unit would bog down in RPM (like
starving for fuel, running down, and recovering right before it
stumbles) unless the choke butterfly was physically held in the closed
position.
After a while, the unit stopped wandering, and settled in to it's 1800
RPM.

The output voltage, however is around only 100 volts AC, and may vary
between 95 and 105 volts, load or no load.

Running appliances like the air conditioners will only be successful
for a few minutes. Then the Cruiseairs shut down, with a LO AC error
message on their displays. On shorepower, they run all day, no
problem.

I pulled the full wave bridge rectifier, and checked it with a meter
in the diode mode.
It appears to be intact. I did notice some corrosion from one leg to
the case. Hoping that was it, I cleaned it thoroughly, but no deal.
Still at 100 v max. MAYBE this is breaking down when voltage is
applied, but I doubt it.

What's the next thing you would look at? I'm thinking an electrical
problem now. How would one check things like the windings and the
diodes?