No, you DON'T have a lot of
solar. At least not when we're talking powering a fridge.
When running at 12v your fridge draws about 10 amps, or 10 amp-hours/hour. Unfortunately, we need to run our fridges about 24 hours per day. That makes 10 amp-hours/hour x 24 hours/day = 240 amp-hours/day. Your trailer has 2, 70 amp-hours batteries (lead acid, I assume) that you don't want to run much lower than 50%, providing about 70 amp-hours of the 240 your need per day. Your lithium batteries can be drawn to 75%, giving you another 150 amp-hours. Together, your batteries provide a total of 220 amp-hours/day, which is about 20 amp-hours shy of what you need for JUST THE FRIDGE.
[Aside:
Hmm...I wonder if that fridge calculation includes the 0.5 amps required to run the control circuitry? If not, that's another 0.5 amp-hours/hour x 24 hours/day = 7 amp-hours/day.]
If you figure out the cabling, etc. I suppose your proposed solution would be maybe-sorta-but-kinda-iffy solution. Rain and clouds will dampen your plan, as would all the other electric draws (parasitic and useful) you probably want to fulfill.
I've read that average
solar RV'ers use 75-150 amp-hours/day day. My wife and I own a 17-foot
Casita and limp by with 200 watts of
solar and a single 85 amp-hour lead acid
battery (curse you,
Casita, for making a 1-battery enclosure when there's room to make a second bay just to the rear of the factory bay). We conserve as best we can and rarely drop below 50% discharge, using 40-50 amp-hours/day. If inclement weather is in the forecast, we spend a night at a campground or RV park to charge with shore power, fill the water tank, and dump the other tanks. We also bask in the air-conditioning for a night.
Eliminating the big electric draws is possible. Namely, we kiss goodbye the A/C and
microwave, running the fridge, water heater, and
furnace on
propane. The remaining big draws are things that have moving parts - fans especially. I learned my CPAP draw can be reduced from 5-6 amps to 2-3 amps by turning off the humidifier and heater. After a couple weeks of getting used to this configuration, I'll never go back - even at home.
The other major electric draw is for recharging our electronic devices. We've learned to charge in the tow vehicle when the next day is a drive day, and also to charge using the "extra" solar capacity that is unused on many mid-late afternoons when charging is in it's final stages. My Bogart Engineering Tri-Metric
battery monitor tells me how many watts are going unused. I love that device.
As others have said, there is is ONE BEST ANSWER to you issue. Explore your hesitation with
propane and see if you can overcome your reservations. You'll never look back.