Thanks for the all the input. I guess I should have added I have a 2016 Ram 2500 as a TV. The dash shows alternator voltage; although I don't know how accurate it is, the voltage does vary as I'm going down the road. I've never seen it go over 14V though.
As I have an older PD4590K18L (not the LS8 version) power distribution box that as far as I know doesn't have a charge wizard function, I will be upgrading that when I go to new Lithium batteries.
I have a brand new Honda EU2200i that I converted straight away to propane (never touched a drop of gas); terrific conversion BTW! My wife is very sensitive to smells (especially petroleum-based products).
I also have a Point Zero Energy Titan solar generator with ground-based solar panels that I have successfully used to power the RV.
I installed a SoftStart on my AC once I found out the Titan & Honda wouldn't run it. After that, everything runs just fine.
Since I'm on a tight budget, the plan is to allow either shore power, Honda, or Titan (in conjunction with the new Lithium-compatible PDI) to keep the new battery (or 2 batteries when I can afford it) topped off when we are parked, and then allow the alternator to maintain the battery(or batteries) to at least 90% as Daryles suggested when rolling down the road, all the while crossing my fingers that the alternator stays healthy. If it doesn't, I'll know the other half of you were right.