A friend of mine and I were talking at lunch tonight and just throwing it out there that we could get a remanufactured battery from a Prius or something and have all the capacity we need. That would be a spendy battery, though. I'll bet somebody has done it.
Somebody mentioned a 12V plug near the TV. I do have one. Unfortunately, I don't have a 12V TV. I might think about replacing it with one. That would solve that problem.
About the solar, I do have a controller in the hallway. I've never checked it with the disconnect open. I will do that. It does show a numerical voltage readout for the battery. I think. It usually reads 13.4 day or night. Seen it as low as 12.6 before. I guess I'll need to trace some things out. I do have a multi-meter, so I'll cross check it.
And, yes, if I add an inverter, I'll do it close to the batteries with thick cables.
Thank you all for the info.