Ok I know this is a bit late to respond since the OP probably did something about that iPad, but in anycase, I sort of found the solution!
I believe it is something to do with the actual connector on the logic board that the digitizer plugs into. What the OP described is exactly how this iPad that I just received works.
First thing I did was test it out and restore it to iOS 7, still acting crazy, some zoom option trying to prompt me to enable it, but the touch is unresponsive. So I turned it off (power plus home buttons together for 10 seconds), got my handy blow dryer, suction cup from the shower hanger, lol, a tiny philips screwdriver, 12 pack of soft nylon guitar picks, rubber gloves, plastic wrap, and a can of compressed air.
So I fired up the blow dryer on highest setting, ran it around the digitizer's frame, popped on a suction cup on the right side, lifted up the glass a bit to insert the first guitar pick, and swayed it a bit to place 2 more around it, slowly making my way around the digitizer and popping it off.
Unscrewed and disconnected the LCD, wrapped it in plastic wrap to keep any dust particles off, wrapped the digitizer and unplugged it.
Cleaned the digitizer contacts, replugged and turned back on, same story, tried unplugging and replugging again, same story again, eventually I lost hope and thought of either bringing it to Apple Store or if not then reselling it on ebay (boy do these sell in the worst possible conditions).
Anyway, upon assempling it back together, I applied some heat to the digitizer again while putting pressure around the frame of the digitizer. Once finished, I let the iPad cool off, then turned it back on and to my surprise it started working again, startled I continued to set it up, but after a few minutes of use, the ghost touch came back and the screen would be rendered useless pretty fast, so thinking the heat may have something to do with it, I used the hairdryer on it again, and then pressed on the glued parts to ensure a tight bond.
The iPad again started working smoothly with no glitch effects. after another 10 minutes the thing started hiccuping with the dreaded ghost again, so I picked it up and tried applying pressure asymetrically holding diagonal corners and trying to give them a slight twist in opposing directions, it seems to work now, hasn't glitched for a while, but my guess is this has to do with the digitizer connector on the logic board itself.
I'll open it up if it starts glitching again and try the alcohol/dusting method to the digitizer plug. Maybe a bit pressure to the plug is necessary, some of these plugs are actually metal framed so if the contacts aren't fully touching the flex cable of the digitizer, the ghost touch will happen.
I've had another iPad 2 that I bought off ebay which had cracked digitizer and dented corners. It had the same phantom/ghost touch thing, but not as severe, I do remember seeing the chassis a bit bent out of shape, so while bending/applying pressure at diagonal corners, I was able to allow proper electrical flow at the digitizer plug, which resulted in a fully functional digitizer.
Honestly I don't understand why Apple chooses to build iPads with slide-in flex cables rather than clip on plug-in like on the iPhones and iPods, this eliminates the guesswork of whether the digitizer plug is bent or not, or if all the parts of the plug are touching onto the inside of the socket.
Well hope this helps any of you. If my problem persists, I'll do a test on the digitizer socket, seems like it's the culprit of the whole thing.