Thanks for the cheeses.
Another tid bit of information on ultrasonic units. The warmer the water in the tank, the more output. I originally wanted the whole unit outside the cave altogether. That would free up cave space and provide for warmer water in the tank. But that introduces new challenges like air filtration, air leakage/cleanliness and a stronger flow.
I found a 3/4" one way check valve used in aquarium plumbing that has a flapper door that seals quite nice and would not allow cold air to escape when the humidifier turns off. But it requires some psi to open properly. One solution is a high pressure blower fan but they are very loud like a vacuum cleaner. The valve needs about 30-40 psi to work properly. After reading up on the humidifiers used in large commercial caves I learned they use compressed air in most of their units. I have an air source already and with a simple 110v solenoid valve it should work. Of course a separate regulator and filter would be required. I will be experimenting with this.