How can I attach a new drain to a drain pipe that's fallen away from the tub?
Yeah, you're in a spot of trouble. There's likely a nut around the flange of the waste pipe that you need to turn as you hold the drain flange in place. 

If it's not possible to get behind the wall where the drain is, how about from below? Crawlspace / basement / first floor?

Even if you could get the threads started, you'd likely end up with leaks if you're spinning the drain flange- you want a thin bit of plumber's putty under the flange, and spinning the flange would likely lead to a broken seal and leaks.