Well, everyone's given such good ideas, it's hard to add anything. I do like the idea of meeting with each of your "chiefs" on a regular basis so you can swing each of them back on track. And I especially like Energizer's words of advice because they offer some stress relief, which you obviously need.
Your situation reminds me a bit of the game badminton, and you, my dear, are the "shuttlecock" (see illustration!)
www.m-w.com/mw/art/shuttlec.htm. The whole idea for your people is to score points, and they don't care if you get caught in the net everytime they try to slam you "home" for the point, well, that's too bad. Sure does sound like you're "in the net" quite a bit.
Your mission (if you should choose to accept it) is to refuse to be the "shuttlecock" and make everyone play nice and keep the game going. I can't really tell you more than what's already been posted. Just use TAA to vent, take a breath, and go back into the game a little fresher and more resilient. As long as you keep in mind that you're the adult here (obviously) and act accordingly, you'll be able to make it until you reach your six-months turning point. Then see if things are better or worse, and if you can live with it or not.
Good luck, and please count on everyone here to give you a push when you need it.
Robbie