You've done everything you should have. Reboot and restore, so I'm afraid it's unlikely anyone will have any solution for you. That said, I have one idea, which would involve deleting apps one by one to see if you have an app that is somehow causing your issue. You won't lose the apps, as they can be re-downloaded anytime. If that doesn't solve the problem, it's time for a visit to the Apple Store.
I had this problem with my ipad. Typing on its own, changing page size, moving about in applications etc, I spent days working on a fix and have finally solved it.
I hope this benefits others;
1) Download latest itunes to a computer.
2) Connect ipad to the computer using white usb cable.
3) Transfer all purchases etc.
4) Disconnect from itunes.
5) go to settings on the ipad and choose the General option, scroll to bottom and select Reset.
6) choose erase all content and settings.
7) reconnect the ipad to the computer. wait for itunes to find the ipad.
8) on the ipad select set up as new ipad etc until it shows the icons.
9) on itunes select restore ipad.
10) leave itunes to download the latest software. it might take 30mins. dont touch it.
11) when the download is complete it will restore the ipad with latest software.
12) go to settings and switch off Bluetooth. turn off Multitasking gestures. select keyboard and turn off split keyboard. turn off the following too; auto correction, auto capitilisation,check spelling and shortcut.
that's it, ipad should now be problem free.
post here if this helps you.