With my converter off, I put my meter on battery positive and the other end of the house side of the breaker. There was 5V difference. My wife turned on the furnace and the voltage differential climbed to about 7 volts fairly quickly <1 min then the breaker tripped.
I put a jumper cable on the battery and connected it to the house side of the breaker. No problem running the furnace despite battery getting down to about 12.7V by now. Moved the jumper cable to battery side of the breaker and it tripped immediately. To me that meant battery disconnect is not an issue - it's the breaker.
Got a new 50A breaker from the local auto parts store and installed it. There was still a drop of 3.5V across the new breaker but not as bad as before. (the drop across the disconnect was 1.5V of the 3.5V)
Anyway, with battery still not charged and converter off, and some lights on, the furnace has been running for the last 15 minutes. Not definitive, but it's a pretty good bet we've nailed it.
Charge battery now - longer test later.
Thanks all y'all (we're still in Texas).
