Dudeness - Thanks for your post. I was looking into the Enerwave unit and was hesitant to purchase it until your post.
I too installed mine as a Multi-switch and it works fine.
Being an electronics tech. I have tested mine prior to installing permanently and believe I have an answer for you.
I attempted using a 24VAC power supply from ADEMCO.
I was unable to get the unit to power and function. I also tested using a 120 constant input and triggering with 24 volts.
The unit powered up but the 24 volt inputs would not trigger the 120 output.
The issue with the multi-switch doing what you want is that it requires a 120 volt constant AND 120 volt triggers.
Suggestion:
Now with a simple SPST 120 Relay and a 24vac Power supply. Powering the Enerwave from the 120v and the aux output will trigger the relay. switching the dry contacts which you can use to switch the 24 vac.
Good Luck