When reinstalling the cover, ensure the top edge of the cover is first pressed up towards the top edge of the body at about a 10-15 degree angle before pressing down on the cover to ensure the whole cover snaps in place properly.
I put the iPhone body’s back (with the front touchpad face (still connected to the body at 45 degree angle) attached by rubber band to a soda can) on a heated heating pad as others suggested. After two minutes I pried up on the left side of the battery with the prying tool in the convenient space just below the volume controls. I worked it slowly and within a minute it was fully peeled out.
When removing the connector bracket note that there is a small square black barrier pad on the undersurface of the bracket at the lower screw location. I suspect this is to prevent the metal bracket from touching the material below it. So, ensure when reinstalling the bracket that you reinstall the pad also.
This went easy. Place the opening tool in the seam near the earphone jack to pry as others have stated. Also, as insurance I wrapped a rubber band around the top end of the phone (covering the listening speaker and camera lens) so if the cover suddenly popped open when pulling the suction ring, (which it did!) the cover would not pop entirely off and damage the connector ribbon inside.