I also used the fishing-wire “cheese-cutter” method and recommend it! I performed steps 1-4, and used the garrote to free each cell away from the tape, then used q-tips dipped in acetone for adhesive residue cleanup. My original battery was swollen (trackpad wouldn’t click anymore). The swelling had already torn some of the tape, but what remained was still strong. Skipping full disassembly saved me a lot of worry and aggravation. The internal connectors are tiny, fragile and get brittle over time, I didn’t want to risk damaging them. The whole repair took about two hours (including photos and adhesive cleanup). I think it would have taken at least 6 hours if I’d attempted a full disassembly. I used an OWC-brand replacement battery. My MacBook Pro started right up first try! It took another twelve hours to properly condition the new battery (charge fully, discharge fully, sit for five hours, then charge fully again). My old mid-2014 15” retina MacBook Pro is as good as new again!
These instructions neglect to mention that there are two hidden clips on the left side of upper case. They are just like the clips in the battery compartment, but they are hidden from view (they are above the hard drive compartment. So it is necessary to not only pry the bottom case out a little, but also to find the two slots where those clips are engaged, and push them in slightly (with a small nylon pry tool, or very gently with a small flathead screwdriver). You can see one of them in the photo above just to the left of the the trackpad, but the one on the left is blocked (in the photo) by the person's left thumb. It's pretty much in the same location as the two in the battery compartment, just on the left side. Good luck. Took me 15-20 minutes of increasingly more forceful prying before I got lucky and accidentally found the left clip holes. I wish these instructions mentioned them... I've edited them so they do now.