It's about 15 ft of cable, but we can't see any of it. It's under the floor, then goes to a relay which we can see, then to the batteries.
if you can't see the wire, how do you know its 2gauge all the way? based on your voltage drop, I'm not sure this is the case
you need to determine where this 6A load is, that's not normal, has nothing to do with old wiring (my rv is from 1999, and the wire is fine shape).
you need your dc clamp meter to measure the difference between what your shunt is saying is going into the batteries, and what is coming out of the converter.
There is NOTHING wrong with your converter, I own a 9245 from them, and it outputs even more then rated.
again you need to determine how many AH in a day your consuming (this is where the shunt comes into play, it will track usage)
once you determine that, determine why your not seeing the 60A at the batteries, and determine where this 6A phantom load is coming from.
THEN you decide how long you want your generator to run, to replace the AH your using per day. You will probably be stacking chargers. Your bank is capable of being charged between 500A to 1200A.
doing any of these steps out of order will simply waste your money.
to answer your why can't I get past 13.6, simple. the charger is not giving enough amperage to replace what your using per day. you need to find all the loads and see if they can be reduced, if they can't we need to make sure the charger is outputting its max amperage. If it is, then we start adding chargers till it can get to full everday or every other day etc.
every single setting I told you in your BMS is NOT going to fix any problem, this is simply getting the proper limits in place. Fixing the loads and the charging concerns is where you need to focus
and again you said breakers, provide a photo of your breakers and dc fuse panel, breakers are not what are causing your issue, its will be on the dc side