Well, assuming you have quality lugs and thick cabling, they would probably easily take 100 amps or more at that level of discharge. In fact they might even draw the max charge current of 125 amps from the your inverter-charger briefly.
I have two 6v batteries with #4awg wiring that is short in length. When I have discharged them to about 60 percent they will draw the max Prog dynamics converter output of 45 amps easily. I charge them with a honda eu2000i. That honda generator could probably run a PD 60 amp converter at full output no problem.
I don't know the specs of your inverter charger, but chances are it could overload the honda 2000 when batteries are discharged that far. However, there might be some settings on your inverter-charger that could prevent that. The only way to know is to try it out.
if your inverter-charger is this model 'MSH3012', there may be a way to program the settings to limit max shore power amps to a level the honda can provide continuously (under 15A AC).