I poured isopropanol into those lowered areas but unfortunately it soaked up along the battery leads and got all the way under the keyboard and elsewhere where it shouldn’t. It made some other plastic parts of the computer swell which isn’t good so I would not recommend pouring any solvent in there. Add a very small amount of solvent (0.25 ml) just enough to soften the adhesive, and let it sit for about 30 min and then pry carefully and add a little more, making sure it doesn’t get soaked up by the battery leads.
Another important thing: when you buy a battery, make sure it’s new, up to 1 year from date of manufacture because they have a limited shelf life and get permanently damaged when sitting uncharged.
You do not actually have to remove the screen to replace the battery. Just tilt up the screen at a 60 degree angle from the phone and tape it open or have someone hold it up. That way you don’t have to flex the screen wires or inadvertently damage anything.
Just wedge the sharp end of the forceps between the bracket and the plug and push until the bracket pops open. That way there is no danger of tearing out the entire socket.