Just wanted to report back. Thanks again for all of the input.
Turns out the cheap cord from amazon had gone bad. I connected the fridge to my cable used for my swamp cooler and everything has been working great. The cable is something like 25 feet, 16 gauge. Even at this length, I am seeing a voltage drop about half of what I was seeing with the other cable that was much shorter. I also cut off the cigarette lighter like plug and hard wired it, since I was worried about the connection as well.
Just checked the voltage of the battery this morning and it was at 12.6 volts, so it looks like everything is fine and overall the fridge/freezer is using much less power.
While working through this, It made me worry about only trusting solar for power. I am about to head out on a 7 day trip to northern nevada (burning man) and wanted a backup plan in place. So in true overkill fashion I purchased a honda eu2000 and a battery charger just incase.
I could have wired in an isolator, but I didn't want to run the noisy diesel engine. Also, i have wanted an excuse for a generator for a while.
I didn't realize how difficult it is to get a battery charger shipped to california. Gave up online, went to the local auto shop and bought the most expensive one they had ($140) since it looked liek the only one that had multi staged charging and let you select battery type.
It works well, but I don't like that I either have to select the 30 amp boost or a 6amp charge that will go to a 2 amp maintain. Is there any good chargers out there is the same price range that will do the 30 amp and then go to the 6/2 amp charge/maintain? thanks!