You only need a 300w inverter for what you want. You can get a PSW if you need one for special items being charged, but a TV/dvd etc is good with MSW.
It should go close to the batteries to get the most out of it using short/fat DC wiring. You can just plug the shore power cable into it (with 30/15 adapter of course) and turn off (unplug) your converter, put fridge and WH on gas (not auto), and your receptacles will work just like on shore power.
TTs are a problem where the batteries are out front and you want the inverter in out of the rain and not get stolen. Some just put it in the front cargo bay and drill a hole in the floor to run the wires down to outside and then forward to the batteries on the tongue. Other solutions may be available in your rig, no idea.