If you feed the panel directly, you'll have to remember to turn off the converter, set the fridge for propane vs. AC usage, turn off any electric water heater element, etc. I think it would be better to have a transfer switch just for selected circuits so that you have fewer things to remember.
However, it would be possible to wire it as though it were a generator and use the transfer switch you have as it is. The inverter would have a time delay before the transfer switch switches, and there would be a minor load from the transfer switch relay coil. This gives the inverter priority over the shore power connection. (It would also be possible to reverse the connections and make the shore power have priority; I'm not sure there's much of an advantage to either setup.)
For just TVs and chargers and such, you could get by with a much smaller inverter, and consequently lighter wiring to the batteries. If you have only one or two batteries, you'd be very limited in how much full power use you could get out of the big inverter. The coffee maker and microwave require a lot more power than the electronics.
