I have to correct myself. We have a Coleman AC.
But the principle is the same.
Look at the part number of your existing thermostat and look for a digital replacement.
Here is an example of what you can find on RV Parts Country:
https://www.rvpartscountry.com/Upgra...xoCBZ4QAvD_BwE
It sounds like you already replaced the thermostat so it should be easy for you to put in the digital one.
Coleman or Dometic, the digital thermostat made all the difference for us. It reacts within 1 or 2 degrees now.
I bought ours from AdventureRV.net.
A search on their page brings this up:
https://www.adventurerv.net/advanced...tic+thermostat
Good luck! This should do the trick.
Kreg