"I have a small 110 volt reefer that draws 168 watts. I think my 400 watt inverter will start and run it. My house bank is 430 amps so I am O.K. there."
OK means just what? Overnight at the hook?
With the usual wiring and inverter in efficiencies 168W will frequently cost 16.8 AMPS of 12V .
Your 430A bank can have half 215Amps used , if the 430A was at the "20 hour rate".
The only questions left is ON time , how many min an hour does the fridge run?
If its the usual crap house unit the insulation will be minor , so figure 50% on time .
You MUST switch off the insulation heaters (the no outside condensation feature) if installed.
DO the math and see if it all works for you.
With a std car style Volt regulator it will take 6+ hours of running to get the batt set ready for the next use.
The 3 or 4 stage V reg , WITH A TEMP SENSOR, will cut this down a bit.