I know this is really old and probably no one has a SP1 anymore. Just adding some more tips since I finally took my cracked screen off.
My glass cracked, touch didn't work, but pen did. LCD was still ok and I was hoping to replace only the glass if it was possible. It's very difficult to not damage the LCD if it's your first time doing it. Mostly because you don't know how far the adhesive goes. I would say about 1 cm, so if you're hoping to save the LCD, don't go further than this when you're inserting guitar picks. The bottom doesn't have as much adhesive as the top and sides.
It took about an hour for me to take the screen/glass off. As others have mentioned elsewhere, remember to go above the plastic bezel, below the glass.
I used a heatgun on low with a wide spreader tip. Taped the screen incase of glass shards. Heated until the tape started to melt a little (maybe ~7 seconds) , then an additional 1-2 seconds longer with the heat. Then I'd use a metal iSesamo to separate the adhesive and stick a guitar pick in. Move the iSesamo over, repeat heat and guitar pick.