Your weight numbers are very close to my 2007 Challenger (29TRL) and 2011 F350 SRW Ford. Just a little under 21,000 total and a little less than 10,900 on my trucks 11,400 GVWR. All less than their spec maximums.
I wonder if the problem really is the modified sine wave inverter? Everything worked when plugged into the 120V AC but not the inverter? Where was the antenna getting it's power from. You know the little switch you have to push before you can get any channels? I'll bet the antenna doesn't have any power.