Whew. It sounds like your batteries survived, though they are low. Your converter is not the best "bulk" charger. Yes, it is an OK float charger. If you have a plug-into-the-wall three-stage battery charger, that would be the best way to get the batteries back up to full charge, rather than just plugging in your trailer to the wall. Your 6 volt batteries at a full charge should be around 6.3 to 6.4 after a 24 hour rest after charging. It sounds like they are still balanced.
If after charging with a good battery charger, then allowing them to rest for 24 hours, and then if they are still only giving you around 12.4 volts together, you might start thinking about replacing them.
Or not. I suppose that you are using golf cart batteries and have over 200 amps hours together. You'll just have to try using them the way you normally would, and if it seems that they are not lasting like you expect, let that guide your decision.
2012 Rockwood A128 (no S)
2016 Ram Outdoorsman 5.7L Hemi 4x4