I did it!

crwdns2853023:0crwdne2853023:0

My old battery was already sputtering.

crwdns2853024:0crwdne2853024:0

I was able to do it! At the ripe old age of 65! I was able to take a photo of the unpacked stuff, but I was so excited with the repair that I forgot to take photos of me doing it. Oh, well. Next time. :)

crwdns2853025:0crwdne2853025:0

Just follow all the instructions on the iFixit site, and you'll be fine.