I found it easiest to use two suction cups. One on the front as directed, and a second one on the back. Give the spudger to your assistant, and have them slip it in place while you pull the display from the case.
I found it easier to pull out one strip at a time. There really isn’t need to pull all three at the same time.
I found it easier to place the adhesive strips on the bench, and then place the battery on the strip.