Brian -

There are latching relays - that lock in to one state or the other until energized again. All the things you're looking to accomplish are do-able.

It may be easier to reverse the power on your DICM. Have the buzzers rest on 10VAC and then switch ground through the ICM. This way (if you have all the grounds in the Power supply commoned) then you can use relay that has a 24VDC coil (using B Battery off your Power Supply).

Sam