First of all, thanks @marcelflueeler and everyone else who gave advice on skipping ahead. This is definitely the way to go if you're just changing a battery! Once you've unstuck the battery you'll find you can't pull it out because it's stuck at the terminal though. Don't try and force it here! You'll need to return to step 88 and soften the logic board adhesive so you can pry it up about a cm, then you can lift the battery terminal up and over the locking post that's holding it in place. I didn't realise this and broke a piece of plastic off the old battery terminal, which got lodged under the logic board and prevented a good battery contact until I realised and retrieved it.

An important note - as per the comments lower down, you can skip ahead to step 95 (unsticking the battery) just fine if you're just changing the battery, but after you've unstuck the battery you will need to go back to step 88 and soften the logic board adhesive so you can pry it up about a cm and lift the battery terminal up and over the post to remove it. I didn't realise the post was there, and broke off a piece of the original battery terminal that got stuck under the logic board. This prevented a good connection with the new battery, and caused random restarts after I put everything back together until I realised and went back to recover it.

When you come to screw this back together, do not overestimate how little force it takes to strip the thread on this #000 screw. I did, and I now I can't screw this back down and have the problem where the iPad restarts every 3 mins 20 sec after you turn it on due to a poor connection here. I've used card to pack this out so the LCD puts a little clamping force on the terminal once you screw it back in, but it's not really enough so the iPad still suddenly restarts occasionally.