Any tool used to pry on the battery connector must be non metallic, to prevent unintentional short circuit between the connector pins. In my case, my index finger nails were strong enough.
The keep the pressure on is on point. In my case once I loosened my first screw I thought I could relief my initial pressure. It was a mistake. I was doing the whole thing very slowly as a precaution. That helped me notice that the Phillips screw driver was sliding up out of the screw head. Not being sure why, I put pressure back on the screw driver until almost all the screw was out of the hole. Once out, I examined closely to find out that the threads have some sort of coating. It looks to me like some kind of locktite. Then I understood the importance of keeping the pressure on all the way through. It made me uneasy having to keep so much pressure on such tiny screws, but I found it was the only way to prevent damage to the “slots” on the heads. Anyway, all of them suffered some degree of damage, but I was able to successfully remove them and reinstall all of them back in their original holes.