Our rig is older, and had two different batteries, one from Les Schwab Tires and one Interstate when we bought it.
I felt as you do that the voltage wasn't coming up under solar charge (90 w portable), and dropping too much under load.
The water levels were full.
At peak while charging the batteries should get above 13.5 volts, and even to maybe 14 v. At rest the battery should sit around 12.5 or so, not under charge, nothing on.
(please correct me if I got the numbers off).
The two 6v golf cart batteries should be able to easily run every LED light in the rig all night long if needed. And the pump or furnace will draw them down, but not to zero volts, and the draw is temporary. The voltage will come back up when the load is removed, maybe not all the way back up as you are using the stored power.
We also run a 22" TV and DISH receiver, mostly in the evening through the inverter.
I have only gone over one night between charges, but I suspect the batteries could last 2 even 3 nights depending on what you are running.
I have one of these plug in volt meters. I lke it better than the panel lights.
Amazon.com: INNOVA 3721 Battery and Charging System Monitor: Automotive
In the end, I went to Costco and paid $84.00 each for two brand new 6v golf cart batteries (exchange price) and now there is no question. Peace of mind.