Quick update in case someone else has this problem in the future:
The symptom that I originally had was that the chassis batteries would go dead even when plugged into shore power and charging via the inverter/charger. I found that the inverter/charger would settle at "Float Charging: 12.6V / 0A". Consequently the Big Boy Relay would not engage and the chassis batteries would not charge when plugged into shore power.
This was caused by the Battery Temp Sensor reading 151C which would shut down the normal ~13.4V float charge since it indicated the batteries were overheating. Normally you could just disconnect the BTS cable from the inverter, and the BTS should then default to 25C and operate normally. In my case, it still registered 151C even with the BTS disconnected. This could only be caused by a defective Control Board in the Magnum inverter.
I purchased a new control board for $290, and swapped out the old control board. After hooking everything back up, I am back in business with normal inverter/charger operation. (Note - I also had a problem with the Big Boy relay in which I cleaned/burnished the internal contacts which fixed that problem).
Thanks everyone for your suggestions. Hopefully, this could help someone else out in the future.