Inverter installation and automatic transfer switch

Transfer switch wiring is the easy part if you power the entire panel.
As said above you just need to make sure certain items are set to propane or stay off.

Transfer switch has two input and one output.
Cut the existing feed and connect to the input and output. Inverter connects to the second input.

If you want to power a sub-panel so only "inverter" items are powered up it just adds a bit of hardware. Or you can power individual circuits after the panel. Whatever works best for your camping style.