The decision was made for me when I tried to push the bracket in place and it pinged across the room. I think that's the last I'll be seeing of the Touch ID cable bracket.

I used a similar method. First I carefully ran a razor blade around the edge of the phone between the metal case and the glass. With the suction cup attached just above the home button I put the speaker end of the phone on a soft surface and lifted the other end a centimetre or so off the surface. Then I use the spudger to push on the edge of the case. I worked along the case until I could get the spudger under the glass.