Once you get the screen on one side of the tape, just leave the paper on the other side until your ready to put it in the box. Solder it all up and then eyeball the tape,, as you put the screen up to the cutout,, no power needed for that.
also, once you cut the opening that matches the hole, use a sharpie to color the cutout on the tape before you put it on the screen.
Cradle the board and screen connected when you put the taped screen in place. Still no power connected to worry about. Unless,,, you're not using connectors at the battery.