[hbens]

Hank you say you have 2 inverters, have you read output voltage between each other? Could be you have split phase.

(Good Idea Here) If you buy a factory built battery and the BMS is built in then you have no way to program this but if you feel uneasy about it just put a resettable in line breaker to the current level your comfortable with, 150 amp is a good value.

Jack, 
I haven't checked to see if the outputs are split phase. I haven't thought about the possibility of that. The two 115v breakers that feed the inverters are side by side in the breaker panel therefore I suspect measuring the pass through AC voltage between them will be 240v. I'll measure with a voltmeter to confirm.
The inverters are not connected to each other in any way except they share the same house battery bank.

Thinking out loud about possible issues running my 240v mini split off the inverters. If going from shore power or generator power to inverter I suspect the voltage would be 240. If I go from a complete electrical shut down (no shore or generator power nor inverting from either) the output of the inverters would not be 240 between them unless I'm super lucky. I wouldn't put any bet on that. The sequence to go all inverted would be to have shore power or generator power running and then shut the incoming power off.

I'll check the outputs and respond here with what I find.