OP While I've run with propane on for 30 years - regarding Method #4.
To me it's a very poor setup, but will work. An outside plug - really? seriously? You're suppose to dangle your cord outside while you drive? And if you do you'll need a water resistant type of cover. Now you have a whole house inverter - any number of appliances will overload it. YES YOU WILL LEAVE IT ON OR TURN ONE ON so carry extra fuses.
Much Much better to install the inverter with a ATS to direct either the 120V shore power/gen (default) or the inverter output to the refer. This may take some AC rewiring but that should be easy.