Hi fellow frustrated Surface 2 owners. I wanted to chime in on this. I've been experiencing the same problems with the same results - or lack thereof - while trying all the fixes. Strangely, in recent days my touch screen started working and then stopped again and my Type Cover (also experiencing lack of responsiveness) did the same, but never were both working simultaneously. The changes in responsiveness to both only occur after updates and restarts, as everyone has noted.
After being told that both were hardware related and that my only recourse was to buy new devices, I got frustrated and basically told Microsoft support that they were ignoring a pervasive issue, and refusing to acknowledge that perhaps something can be done to resolve this with a software patch. After some back and forth, they agreed to review this very thread, so I sent them the URL and I was assured that they'd take the issue under advisement and work on a fix.
Naturally, I don't assume that anything will actually happen, but at least someone was willing to pretend to care. If they actually do release a software fix, that is just a bonus! If not, at least I tried.