One way to have the I/C shut off and Li battery disconnected from RV 12v systems (but still connected to the I/C and sitting at 80%) and run the fridge is-
to run an extension cord to the back of the fridge outside and plug the fridge into that instead of the RV. (No complication about using the shore power cord and its connection to the inverter input)
Also plug the converter into that extension cord and clamp its 12v output to the fridge 12v input, say at the DC fuse panel. Now you get 12v lights too.
What happened to the OEM converter? If still there and you can have shore power while the I/C is by-passed and the Li bank is isolated, then you can do it all without using the extra converter.