I sent Mr Moom to a chiropractor and tried to knock his knee back in-line:
It's only very slightly better. It still trembles, and it goes out at a slightly different angle to the other one, but I honestly can't figure out what on earth is wrong with it. I messed with the fCurves, tried only animating one dimension of the up vector - could not figure it out. It's as good as I can do for the time being...
I tried to loosen the head up a bit as well. Not too happy with it but it's getting there. I'm probably gonna just go and re-do it from scratch 'cause I used too many keyframes and I've started losing track of where everything is. Hooray!