The multimeter is pretty much a necessity for RV troubleshooting. I found out by experience it is tricky to use for finding battery state of charge. When the battery is charging its voltage says nothing about the battery; it only gives the charger voltage. When charging is stopped, the battery voltage very gradually goes down from the charging voltage to eventually indicate the state of charge 8 or 10 hours later. 12.6 Volts for full charge, 12.0 for 50%. Note that discharging below 50% damages a standard deep cycle battery, which is why an RV sitting unused for a year is likely to need new batteries.
I would boost the generator with a car battery using booster cables.
I finally found a place that sells Sea Foam - six different kinds. What kind of sea foam did you use to revive the carb?