hardwire an inverter?

IMO you need at least 400 watt, That will require #6 depending on how far from the battery. Go pure sine wave. In my case there was tons of room behind my convertor and lots of ventilation. I built a platform at the rear and fastened it down to that. I bought an auto switching inverter, one that automatically passes AC through when hooked to power and sends AC out when power is not there. I took the runs I wanted to run off the inverter off the back of my convertor panel and ran them through it then back through the breakers on the converter. They feed my TV, bedside plugs and the one I use for my laptop plus pone GFI circuit in the bathroom. I used the existing #6 wire going to the battery. With 400 watts that works, much more and I would have needed #4. To test it i loaded it down with as much stuff as it could handle, plus ran as much 12v stuff like fans & lights at the same time and checked the feed to see if got warm (it didn't, so good to go)

Main thing I had to check was that i removed the fridge from any of the circuits,. You do not want it switching to inverter output when set to auto if the power goes out.

http://www.anchorexpress.com/promariner-pro-trusine-400-power-inverter-79400