Wow! And I thought these stinkin' squirrels and cats were a problem. My heart goes out to you.

I used to work at an azalea nursey and we did all our propagating by soft wood cuttings in the spring and summer so it can be done. We just put them in flats and covered with plastic for a few weeks. I know people bag them and hang them on their curtains (what the?) too.

Here is a site that gives the details.

Also comisserate here. Most of the posts seem to be from those with diseased or dying azaleas but I actually think yours will come back if there is anything left of it. Be sure and give those kids' parents some of the rooted cuttings next year.