Choosing a new house battery

Well thanks for staying on course for believing the problem might be my inverter/charger. I am not sure, but I ran a bunch of voltage tests and you might be right. If it is the Progressive Dynamics unit, then I still would have to make a purchase, but I could hold off on the battery. I sent a memo to Progressive wondering if there is a "smart" unit that can sense and handle both Deep Cycle AGM and LiPO4 batteries. I might also give e-trailer.com an email to see what they say. They have been excellent in the past with getting back with their tech. support. I will also still check on Li batteries, just in case.
Thermmoguy: Thanks for your story. At night, when I put my scare lights on or too many interior lights they all dim too.