I live in a 2005 Damon Intruder 377W
The original Interstate U-2200 (Which is right close to what you have) would last, as I recall, most all night with lights, furnace (if needed) and the inverter with TV's off (Night being 10P to six Am or 8 hours)
I eventually added a pair of MK G-31 AGM's for the inverter, but they did not work out well, defently a bad idea to go AGM.
I now run a pair of Deka G-20's (slightly bigger battery than the one you have) wired for 12 volts, and in parallel with them are three Group 29's. I can even watch TV most of the night, run computer and such.
Home is where I park it!