Its totaly an art to take the screen from the digitizer (1st gen 2012 Nexus7). But I found out a trick.
But also in end I broke my good sceen. to bad it could work as a digital fotobook (you can use a mouse with an USB-OTG stick)
Here is what I foud out:
The surgical adhesive (glue-tape) is only sticking well on the digitzer. not to well on the plastic. The Screen only sticks a bit on the edges. I tryed it without heat, worked well! the big different is, you want to grap the tape between plastic and digitizer (I have done it with a realy small screwdriver (flat ;-) !) and pull it out to the side of the frame.
You can image it like a magnet on a metalplate. Dont try to pull it, you have to sweep it to the side over the edge of the metalplate.
there is no need to take a string all the way throu the display and end up with the glue on the screen. If you like to take the way with string (like in other forums / users) remember, the glue-tape is only behind the plastic, so stopp before the screen starts.
Hope this helps. good luck.
mani