Have you yet determined that the voltage that what you are reading inside the coach is the cranking batteries? Because my guess is that is NOT and that your reading the house batteries voltage and not the Cranking batteries.
Have you properly tested you cranking batteries as of yet?
Failing to do so IMO will only lead to a guessing game and yes sooner or later you will probably get lucky and find your issue.
Hopefully this doesn’t come off as being critical I / We are just trying to be helpful.
A simple logical and well thought out diagnostic strategy along with a Digital Volt Ohm Meter with a ( Min- Max) function and a set of very long homemade leads will lead you to the promise land and most likely pretty quick.
The diagnosis starts with knowing whether the CRANKING the batteries are indeed Good and to the proper spec.
So if the battries are tested properly and to mfg spec and they are GOOD , we then take our volt meter and do voltage drop test from the positive and negative battery POSTS to the starter positive POST and starter case. Battery voltage drop tests are very simple to do.
So at this point you now know that the batteries are capable of doing their job properly and that the electrical connections are capable of doing their job from the cranking batteries to the starter.
My guess is that you will have your answer in these simple tests and pretty quick.
If not? On to some starter motor tests.
Cold ambient temps cranks slow …….after warm is O.K.
hmmmm engine oil weight issue perhaps? I doubt it but just a thought.
Happy Hunting