Chosen Solution
Some people suggest that it is not necessary to remove the speakers, airport card, etc. to make a battery swap, suggesting that doing so is more likely to create a problem. Both iFixit and MacSales’ tutorials have you disassemble several items, why? I would be interested to hear suggestions as to why one way or the other is better. Update (07/24/2018) Replacement battery was installed this past weekend, absolutely no issues. I went into it with Dan’s advice in mind, but once I opened the case and saw exactly what was there I proceeded without removing the multitude of parts as per the instructions. Taking precautions to keep the glue remover away from all but the battery, I was surprised how easy it was to get the battery out. I used dental floss to gently saw back and forth, the first cell came out in less than ten seconds, I then loosened the other three small cells. When it came to the two large cells in the middle, I tried removing them with only the floss and no liquid remover, it seemed to work just as well without the liquid remover. I think the floss cut so well that the remover really wasn’t necessary. Overall a very easy job and I felt much better not having removed the other stuff.
Sadly you do need to pull the speakers to make room to get the solvent in and get the battery out. If you left them in you would get the solvent onto them damaging them! It’s a required step.