I have never had a concern with humidity, not indoors or outdoors. Humidity is water in the air. I have never measured it or felt a need to measure it. Again, not indoors or outdoors. or even in incubators.
What I am concerned with is the ability for monitors to stay hydrated, they normally do not do this with humidity. They control there hydration, with food and behavior. That is, they limit their exposure to air thats too extreme, both to wet and to dry. We provide areas of moist substrate that monitors can control their loss of water with. It really doesn't matter if they are dirt burrowers or tree dwellers, they still behaviorally do it the same. The difference being the use of dirt or leaflitter.
In our desert our reptiles, require finding burrows crevices or hollows, that maintain about 50% humidity. If they cannot find such a place, they are dead. If tropicial monitors cannot find the same, they are also dead, it only takes longer. Actually, the goals of both tropicial monitors and desert monitors are about the same, both want to find neutral homes. Desert monitors, have a task in finding humid enough ones, and tropicial monitors have a task in finding dry enough homes. But understand the goal of the task is the same.
Ok, the simple answer is, we let the monitors control it themselves, thru the use of their substrate. So, I would not be concerned with your move. Anyway, to us, texas is wet, hahahahahahahaha ok the very western part should be considered Az. Thanks FR