That looks a lot like my battery bay but I have 6 - 8D batteries, 2 chassis and 4 house. Unfortunately the previous owner or the truck sales place where I bought it put in all start batteries, no deep cell. I am still investigating what to do about my house batteries (may go with Lithium - LFP) but I ended up replacing the start batteries with maintenance free 8Ds from Sam's. The price is good and they definitely have plenty of locations.
As for your house batteries, I would definitely recommend AGM 8Ds. I purchased the Deka (East Penn) 8D AGMs for my previous MH and get them from a local battery supply house. If you look at the East Penn website they will have a listing for dealers all over the country. I think they have one in just about every decent size city. I went through two Xantrex inverter/chargers on that MH and both had settings in the control panel for AGM batteries. My Deka 8D AGMs were still going strong after 7 years when I sold the MH.
A 20 watt solar panel won't do much other than keep your batteries charged up if you disconnect them from the MH. More than likely parasitic loads will pull more than a 20 watt solar panel will charge in a 24 hour period. If all you are trying to do is keep the batteries fully charged when in storage then it should work.
