I get what you are saying. I believe you are safe grounding the chassis of the inverter back to the chassis of the trailer. This is to prevent possible damage to the unit itself in case of a short. There is no reason to run a larger wire than 8 awg.
However, speaking from experience, DO NOT hook the A/C side of the inverter directly to the trailers A/C power bus (where the breakers are). This will for sure fry your inverter. Don't ask me how I know this. The reason is because the trailer's DC and AC power share the same ground.
If you want to run a set of plugs, i.e. for TV or certain wall outlets you might want to consider a transfer switch or a DPDT switch. This is what I will be doing so I can switch between power, but at the same time keeping the inverter separate from the trailer power system.
