Just to help you out at bit.
Residential refrigerators do not run on propane.
You need to start looking after you measure your opening and then see how hard it would be to remove your pantry.
As to running off your inverter, depends on what size inverter you have, how many batteries you have and do you boondock at all. (also if you inverter is wired to the current outlet behind your current refridgerator)
Not an expert at all and sure other will chime in with help.
2011: 54 days, 2012: 218 days, 2013: 175 days, 2014: 196 days
2015: 188 days, 2016: 72 days,
2009 Berkshire, 390QS, and toad