How good are you working with electrical?
Is money an issue?
Of course transfer switch is the obvious thing that works, but also expensive.
So I can induce a few things.... that you are not running your fridge off the inverter too? Of course not the AC either. Not running a space heater off the inverter? not bc the inverter cannot do it one at a time, but that 600 a/h is not ideal for running 3k loads, so
you are just running other things, mostly just the outlets that you plug your kitchen appliances into, hair dryer for a few mins, coffee maker, stove or other minute-at-a-time devices, plus all the DC loads like lights, water pump and fans (furnace fan that blows propane heated air).
How are you isolating out the 3-way fridge from using electricity when it goes from shore to battery/inverter?
Is your inverter even wired in?
If wired in then how do you keep charger from charging the battery that the charger is running off of?
Exactly what do you need to provide power to when using the inverter? and how (outlets or direct into the inverter plug)?
From these answers we can help better than just saying the expensive answer....
