Another idea is to use an ultrasonic humidifier or any cool mist humidifier. I used one once to provide moisture to a larger-sized vivarium (2x2x4). I found flexible tubing at Home Depot that matched the nozzle of the humidifier, and brought the mist to the vivarium.
I have seen others use PVC pipe to deliver the mist to multipe cages. Small holes were drilled in the PVC pipe at each cage. This was for small chameleon species.
The only problem I discovered was cleanliness. You have to keep the tubing clear of algae and bacteria.
For humidity without mist, Reptile Haven in southern CA used to distribute a product to be used with an aquarium airpump. The air was pumped into the bottom of a sealed container filled with water (through an acquarium "bubbler"
. It left the top of the container as 100% humidified air. A small tube brought the air into the cage. When put on a timer to run at intervals, it worked very well to make the cage humid without saturating.