Get a Kill A Watt and measure the actual power usage and then use the following.
350W/120V is 3A AC draw which is about 33A DC with an inverter, enough for you to pause perhaps. 33A*8h is 264Ah and you'll need 528Ah for a 50% discharge. Two 6V GCs at 230Ah in series is 12V @ 230Ah. 4x GCs is 460Ah, barely enough for 8 hours of Ox. Add 2x GCs for the house.
You need 6x GCs and likely 500W or more of solar.
Adjust the above for hours of sleep etc. But I'm sure you know that that Ox machine uses significant power just because of how warm it gets. You can go with $$$ lithium’s which might also trigger new charger and inverter but can be drawn down to 20% hence smaller total Ah but you still have to replenish the 80%. You can run the gen daytime for some amount of charging. Another option is a $$$ portable Ox machine which use a lot less power and will run on 12V, not sure how they will hold up for continual night time usage.
The bottom line is Ox machines use a lot of power.
2009 Holiday Rambler 42' Scepter with ISL 400 Cummins
750 Watts Solar Morningstar MPPT 60 Controller
2014 Grand Cherokee Overland
Bob