I also have a Jeep, with Solar, but a 2 door. It runs just 40W of Solar on the roof racks and 66AH of dual battery setup in it. This is to run the 25lt Waeco fridge I have in the back. That fridge is purely for drinks when out on the trail so the onboard solar is for keeping the battery topped up if I get back to camp early and park for longer than normal. In reality the 66AH will run the fridge for a couple of days anyway even without running the Jeep to top up the battery or with minimal solar power.
My trailer also has a 105AH battery in it, it runs a 50lt Waeco fridge and sits in camp all the time but has 240W of folding solar (80W shown below when I was testing). It will run 24hours a day, 7 days a week with no additional charging as long as there is 4 hours of good sun each day. Worst case I take the fridge off it and put it in the JK while I'm out on the trailers, this lets the trailer battery charge up with no load.
Fridge in the trailer plugs in here.
Realistically I can't see any situation where I'd need 400w of solar and 200AH of battery, even what I have now is more than required
Oh and I have run my 240V (Australia) drill off of the 600w inverter with no issues. I reckon you rethink and start with less, both in weight and power, get the bigger regulator and you can always add the extra panels later if needed.
Cheers
Steve