Two circuits... go with two transfer switches. First move the converter to a separate breaker. Also verify if the fridge is on one of the circuits. (now I read you have already found that) I put a note by my power switch to put the fridge on propane only while in use.
1200w or 300w is your choice especially if you will soon be moving to 4x GC2.
300w you can probably use existing 12v wire to the battery. Mount right behind the electric panel. 1200w you need to pull 120v wire from inverter close to the battery to the distribution panel. 1200w needs to have short fat 12v wire. I have done both ways.
Install transfer switches. Transfer switches have two input(power source) and one output (load). Remove the circuit romex H,N,G from the panel and connect to the load side (output) of the transfer switch. Connect inverter to the default input and a new piece of romex H,N,G from the breaker panel to the other transfer switch input. Repete for the second circuit. Inverter on and enjoy. Or plug in and it operates like oem.
I recommend sine wave only. 300w I like Go Power and Morningstar. Both have a remote power switch provision. I have and use the GoPower. Whatever the choice make sure there is no issue connecting to an RV distribution system before you spend money.
Also verify full wattage is available at a single outlet if you need full wattage to run coffee maker etc. Some give half power at each outlet.
I recommend the 15a Xantrex Prowatt transfer switch.