So here's an update on this. To answer all the questions, yes, I tried every manner of resetting to factory settings, and also tried manually downloading the update and installing via iTunes.
None of that worked and Apple was firm that the phone was unusable (as stated in one of the earlier posts, they claimed that it wasn't the update that killed the phone, but the update uncovered a defect in the phone). So I bought a new phone and stuck mine in a drawer. This week Apple pulls 10.1.1 and releases a new update, so I tried that on my broken phone and lo and behold it works fine. So now I'm stuck with two phones, and Apple clearly was in the wrong about it not being the update that bricked it.
Will have to pursue some sort of compensation but I won't hold my breath.