I took a serious shortcut and saved a ton of time and effort on this repair. Found some heavy duty mono-filament in the studio, tied the ends to some 1/2" square dowel rod sections, and taped the handles for comfort with some gaffers. I didn't remove the fans, motherboard, or anything other than unplugging the old battery and taking off the two battery terminal screws.

I just tucked used the mono-filament behind the top corners of each battery cell, then held down the computer and slowly cut through the adhesive like a mafia hitman. I found pulling one side while holding tension on the other was more effective than trying to pull both at once. About half a dozen strokes and the cell popped up, and I used a card to snap the last bit of adhesive at the bottom. Repeated for all 6 cells, being especially careful around the one with the track-pad cable. It took about 10 minutes to remove the old battery.

Removing glue residue took a good portion of an hour, a little at a time, using the spudger worked best.