Please do this. Having the search box at the bottom of the page makes no sense to me.

+1 for this. I use AutoPatchWork so it's not very accessible (I can imagine this the same for those not using AutoPatchWork too, though)

One downside of your suggested placement is it would push down page content about 20px. But I agree that the footer is sub-optimal.

Or actually, maybe if it was just in the top bar -- between "submit" and my username.