OP has the cryptic comment " I could throw in an LED lighting load by tripping the main for the panel, and back feeding one side, and It wouldn't make THAT big a difference. For giggles, I plugged 2 of them into the cord as well."
I get that he made a suicide cord (120vac cable with male plug at both ends) , plugged one end into the inverter, and another into a wall outlet. Thereby connecting the inverter output to the loads on one "side" of his split-phase main load center. I guess you'd figure out which side your fridge is on, and then hope the couple of other low-load circuits that have useful lighting loads and stuff like your modem, are on the same side; maybe switch some loads around to different breakers if need be. But, WHAT does he mean by the "for giggles ..." sentence ?
And yes, this has the critical requirement that you turn off the main breaker, to avoid backfeeding the grid. Also want to make sure you turn off breakers for any big loads on the side of the panel you're backfeeding. Maybe have a checklist, and strict instructions not to even attempt it unless you know what you're doing.
2018 Nissan Leaf SV
2006 Subaru Outback 2.5i Ltd