300 watts of solar, plus also being plugged in with converter working 24/7, should have 1 to 2 batteries fully charged very early in the day. AS pointed out, 300 watts will be pretty light for recharging 4 batteries, but you say right now the converter is also charging them. Seeing them at 14.4V in the evening means that the controller does not consider them to be fully charged. The controller could not be properly determining SOC, or there is a load on the batteries which prevents them from being fully charged. CJW8 makes a good suggestion about the fridge running off of an inverter, but you say you are plugged into shore power which means that this is not likely. Any other continuous 12V load being applied like a fridge condensation/door heater?
While a pure voltage reading isn't a full picture of true battery SOC, seeing the voltage at the float level (13.X V) is more indicative of fully charged batteries than the absorption level (14.X V). This is because seeing the batteries at the float voltage implies that the controller completed the bulk and absorption charging stages and has dropped down to float. Seeing 14.X V means it is still in absorption and the controller does not consider them to be full yet. Of course if you are plugged into shore power then the converter is messing up this logic by always being on. I agree with the suggestion of shutting the converter off, let solar do it and save the converter backup use with a generator.
As mentioned, raise the bulk/absorption voltage level to 14.8V with 6V GC batteries.