I gave up with the suction cup as it wasn't working for me with a cracked screen. Having heated the bottom of the phone with a hair dryer with a high heat for a good minute or so, I used a safety scraper (essentially a razor blade in a holder) along the bottom of the phone to separate the screen from the body of the phone. I used the scraper vertically between the bottom of the screen and the phone body and levered it sufficiently so that I could fit the spudger between the screen and the phone body. My experience when I first used the spudger around the frame was that the cracks in the screen caused the screen glass to separate from the frame, so I had to re-do it and ensure that the screen frame was separated from the phone body.
I would suggest that you are not shy with the hairdryer. A high heat on the bottom of the phone for at least a minute, if not more, if required.