I run a small repair business and have also had problems with Z3 (and occasionally Z3 compact) coming unstuck. I think I may have now cracked it :)
I first clear all old adhesive, clean both the frame and the new screen with 99.9% isopropanol and microfibre cloth, I allow to dry then apply TWO layers of the best quality 'original' adhesive cutout I can find to purchase. I add a small amount of silicone glue to the top and bottom of frame and secure the screen in place. I apply a small amount of heat and use little plastic clamps for a couple of hours on top and bottom of screen. This seems to have turned the nightmare of Z3 into a minor headache :)