I would stay away from the OTA Antenna Panel 12VDc Socket. The cheap 12VDC sockets you are referring too is prone to melt down rather easy and then you have another panel to worry about replacing being your OTA Antenna Panel. If you blow this wire and circuit you will not have OTA TV power anymore...
The best thing to do is too install your INVERTER direct wired with its own dedicated FUSE circuit as close as you can get it to the battery bank.
Then you can run 120VAC extension cords from this INVERTER to the HDTV Home Entertainment area and also to your Bedroom night table area for a few 120VAC items you might want to have on when camping off the power grid.
Please consider this drawing I made up for some interested folks wanting to to do the same thing...
a 300WATT PSW INVERTER is a good size to run several items you might want to run when camping off the power grid. I used a 300WATT for awhile and finally ended up with a 600WATT PSW INVERTER but I already had a good solid 255AH battery capacity to operate it.
Since you probably want to operate some electronic items like your HDTV and DVD unit I would stick with a PURE SINE WAVE INVERTER. Then you don't ever have to worry about what might get plugged into it and not go up in blue smoke...
Just my thoughts..
Roy Ken
My Posts are IMHO based on my experiences - Words in CAPS does not mean I am shouting
Roy - Carolyn
RETIRED DOAF/DON/DOD/CONTR RADIO TECH (42yrs)
K9PHT (Since 1957) 146.52M
2010 F150, 5.4,3:73 Gears,SCab
2008 Starcraft 14RT EU2000i GEN
2005 Flagstaff 8528RESS