Isopropyl alcohol + acetone + loyalty card
Battery was completely drained and would not hold a charge after sitting for a few years.
The repair wasn't too bad once I had the right tools (I thought I had a set of pentalobes but ended up having to borrow them). It took a bit more than an hour, but I think I could do it in 45 minutes or so if I had to do it again. I didn't get the kit, so I had to experiment with methods to remove the original battery.
I tried cutting under the battery with thread and twisted floss, and I tried soaking the thread in alcohol. Those didn't seem to be working and required a lot of force to make progress. What ended up working wonderfully was to take a small bowl, put a 50/50 mixture of isopropyl alcohol and acetone in it, dip the end of a flimsy plastic loyalty card in it, and slowly work that under each battery cell. If you just apply consistent pressure and dip the card in more of the mixture when needed, you will slowly pop each cell off the case. When you get close to having a cell off, you can even gently pry it using the card to help distribute the force.