Isolation tape can also be placed over the connection after disconnecting to prevent any accidental short-circuit mishaps, thus reducing the need to remove the battery.
It’s amazing how a heat gun or hair dryer makes life easier to soften up the adhesive. Then use a thin iSesame opening tool to get in under the screen (start @ 90 degrees/vertical either side of the home button & slowly go horizontal) the need to use suction cups. Run the opening tool along the front and down both sides to cut the adhesive before trying to lift the screen.