I looked on the Crown website and your Crown batteries should be charged at 14.5 V
Absorption stage and 13.5 V at the float stage.
I'd say your Parallax charger is not doing the job. You want to make sure that all connections are clean and adequate wire size is installed between converter and batteries. If you have a different battery charger, use that to charge batteries to confirm the Parallax is a dud.
IMO, there are a couple of different roads to take with new batteries and an ancient converter. FWIW, what I did was install a solar panel and I rely on that for charging the batteries, primarily. My old converter is used only when the sun doesn't shine for days and I need some voltage to get me by. The advantage of solar is that it is working every day and the programmable charge controller does a better job of charging than I can with all manner of 120V chargers. My rig is always ready to go, fully charged. For reference, I have two banks of batteries, 2 X 6V and 3 X AGM 12 V. On the roof is one 235 W module. I do have a generator but haven't used it. For Winter storage, the Module is tilted and snow melts off in a day or two. No worries and no battery carrying is necessary.
An alternative is to buy a new converter, making sure you can get it up to 14.5 + volts for those new batteries.
Nobby, you're getting a fast education and the price isn't bad. Most RV'ers would have their trailer at the dealer's shop and be paying up the a** for repairs, waiting patiently in line for months to use their rig. Don't get shook, you're almost there.