Agree, forget about getting the glass off in one try. Apparently the glue hardens out a bit, I couldn't get the screen off with the ordered suction cups. In the end I did the same as Brian above: just kept breaking off more glass until the LCD was free, then painstakingly removed the bits around the border with a sharp knife. Just be careful.
Keep a vacuum cleaner nearby, as you'll end up with lots of microscopic glass fragments.
I vacuumed the LCD then sprayed LCD cleaner on & wiped it with a microfiber cloth. This worked very well. Make sure you get all the glass fragments off the border as well, I missed one and now the border makes a bit of noise if you press down there.