I was able to ply the battery out slowly, without removing the logic board because the battery was so swollen. Just started by prying it out using the side of the case, not the logic board, and it peeled out slowly. As mentioned further down in the instructions, the copper flashing had to be pushed back into shape. The battery unsoldered easily, lifting as described. Just slip the flexible conductor from the battery out from under the logic board.

It powers up without a battery if you need to get data off the iPod.