For reference...Our PC is garage-kept in comfortable temperatures year round. Our first year of ownership back in 2007, I kept the house batteries connected, plugged our PC into 110V, and let the Tripp-Lite inverter maintain the batteries. That was a big mistake because of chronic acid boil-overs.
It didn't take long to conclude the best storage method for me was to disconnect all batteries from the house and chassis, charge them till full, then let them be. Roughly every 3 months, I will put them on a 4 amp charge just to top them off, but I am not quite convinced that is even neccessary. I would likely increase the frequency of charge-topping if the batteries were outside in the below freezing and occasional sub-zero temp conditions we see here near Chicago.
Back to that first year plugged into 110V throughout winter storage, another mishap had occurred. I accidentally had the Hot Water Tank turned on to 110V. With the water system drained, the remaining 1/2 gallon inside the HWT did not protect the 110V heating element adequately to avoid a failure of that heating element. So not only did I mess up the house batteries and tray, but I also had to replace the HWT 110V heating element.
My experience with pairs of 12V house batteries has not been good. I always had one charging and discharging much faster than the other. This imbalance contributed greatly to acid boil-overs because one is getting over-charged while the other is trying to get charged. The weaker battery eventually takes so long to charge (or never gets fully charged) that battery acid is spilling out everywhere.
Switching to two 6V batteries seems to offer some natural protection against over-charging. The two batteries are daisy-chained acting like a single battery. Much like stacked batteries in a flashlight, they supply power to the house in unison, they drain in unison, and they also charge in unison. In my case, I switched to two 6V AGM batteries of which I am very pleased with the results. There are no acid/water levels to monitor, the batteries hold more energy, and they outlast 12V wet acid batteries by 4x and counting. I would get only 2 good years from my 12V wet acid batteries. With the 6V AGM batteries, I got 8 good years so far and am still counting. I bought my 6V AGMs from Sams Club back in 2015 that were twice the price that of 12V wet acid....$180 compared to $90 back then.