Is there any non-polling way to detect when a DOM element's size or position have changed?

You might could do it with CSS animations. Check out http://developer.streak.com/2012/11/how-to-detect-dom-changes-in-css.html and similar. I suppose it won't handle all your requirements though, now that I read through it some more.

A co-worker pointed me to a technique that uses the underflow and overflow events. I haven't tried it, and I have no idea what kind of browser support there is (looks like Chrome and FireFox, and it should work in IE by synthesizing the same events that browser would look for, but I have no idea which versions support the technique).