Well, incidentally, my humidistat just died, about a year after my other post here. Needing a solution, and being lucky that the solenoid still works, I decided to just bypass it with a relay. This ended up being very simple.
Here is the original wiring that went to the control board:
H are just the two wires for the solenoid.
I found this Zigbee relay that allowed me to power it directly from the 24VAC of the HVAC control wires, no USB power required. This, combined with a Generic Hygrostat helper, and a humidity sensor is basically all you need.
Here is how I wired it up:
Using W to power the solenoid ensures that it won’t run unless there is a call for heat. This also acts as a small safeguard in case my control logic is faulty or the relay fails on, the worst that can happen is the solenoid runs every time there is heat vs running 24/7 (including during seasons where heat is not used). You could also use G instead of W, but evaporation off the pad is less efficient without the hot air, leading to more wasted water (and a less stringent safeguard).
One small change I needed to make to get this working with the hygrostat integration: for some reason the zigbee configuration of this device reports the relay as a light, instead of a switch. You need a switch entity to use it in a controller.
Below is a guide I wrote for handling this, as I had not seen this done before:
A final optional step would be to use an outdoor temperature sensor, or a weather service to set the target humidity. For me, this was the original reason why I wanted to do this. But after the humidistat went out, I finally had to get it done.