Voltage drop from solar controller

Batteries still have not reached more than 13.7 Volts when the controller was passing maximum current (19.0 Amps)

thats because the batteries are capable of absorbing more than what is being produced, how much of that 19amps is going to power the RV, how much into the batteries
voltage at the batteries will rise , when they are nearing full charge
high amps low reading at batteries, low amps higher voltage reading at batteries

have you done a power audit, ?
How much power are you using every day
You mention the converter, but it sounds like you are not using any shore power at all except on cloudy days
An rv absorbtion fridge running on electric uses a,lot of power, 350 watts or more
Approx 30amps when cycling, or do you have a residential fridge ?
are you cooking with electric, thats heavy high amps power draw from the batteries

i have the same controller, 505w of solar, and a 120v residential fridge
i run the generator several hours each day usually in the morning to bulk charge the batteries ,Then the solar does the top off and help carry the daytime useage
batteries power us all night

i think you need to have the converter and other needs on shore power , More than you have been doing