I think I could answer most of oldman's questions and I don't think the answers mean much. An important question however is how much water is in your batteries. If they are low it could mean that they are being overcharged and boiling off the electrolyte. I think you may have one or more bad batteries and would have them load tested as a group and individually. If the converter has a pendant, it would show the bulk charge but to drop from 12.5 to 10.7 volts in just one hour is weird and sounds a lot like a bad cell in one of the batteries. Here is the sketchy part, with the batteries being only 36 months old and normally they are rated for 72 months, do you need to replace all four? We used to replace bad cells in our 512 cell battery but only once did we replace all the cells. Then again we had to cut holes in the hull to replace them all.
Making sure all the connections are good after the individual load test is a good idea, if they need water add some before driving over to have them tested. You need to do all those normal things we all forget to do or put off on occasion sometime during this trouble shooting procedure.
Sorry about the curt reply to you but he sounded like he knew a lot about what he wrote.