Hi, really like the battery charging station box. Neat. I love pressure cookers too but got one for use one on a gas stove. Just made beef sharwama in mine this evening. Delish.
Some MPPTs are fairly sophisticated and programmable, mine has an adjustable absorbtion and a float phase duration and voltages. The absorbtion phase is normally only for an hour. So a standard float for 12v at 13.8v might mean the controller is working as designed?
Sounds like the battery is wearing down and the inverter wiring needs upgrading as mentioned by others