Updates -
I bought these items-
I have validated that the Lusatelli 12V LifePo4 battery was able to charge up to 13.6 volts via my solar panel (100w) and the new solar charger setup using a multimeter.
I then disconnected the solar panel and ran the fridge for 40 hours on just the battery - for at least 24 hours the multimeter was showing 13.2 volts (aka 70% capacity according to multiple sources).
At roughly 40 hours it was reading 13.15 volts, which would equate to roughly 50% capacity still - I am quite please with this result.
I also installed a 15Amp 3 prong household style weatherproof outlet on the side of my tongue box so that I can use a basic inverter and extension cord setup to power devices in the near future. I am heading to Yosemite, and figure I might be able to put my fridge inside the bear box at the campsite and run an extension cord to it