Your furnace by-passes the shunt so no effect on monitor's amps reading or its AH count. The converter runs the loads so no furnace load on the battery reducing its voltage.
Yes, Eco has no effect on the gen's 120v level so no effect on converter output.
If the furnace was eating some of the converter's amps and cycling, it would have shown by the 53 amps changing, but that stayed constant. So if it was on it was on the whole time at the same amps.
I just noticed that you must have stopped for 10 minutes at 2:00 and restarted at 2:10,(fixing the hot spot) so that might explain why the first half of that hour from 2-3 was lower.
Not much voltage rise over time in that second hour while SOC went up.
Was a graph of that in one of the links ISTR. Have to look at that cell voltage vs SOC relationship with Li again.