I had to tape most of the cables out of the way while reinstalling the logic board, because they kept returning to their plugged-in shape under the logic board as I tried to position it properly.
The “You don't need to use very much” advice turned out to be a bit misleading. The acetone evaporates pretty quickly, especially if you are actually in a well-ventilated area. The adhesive does need a decent amount of acetone to soften enough to let go of the battery. The battery I removed had a substantial amount of adhesive, so at least 8-10 drops per battery cell was required.
It’s hard to count the number of drops being dispensed while precisely dispensing the solvent underneath the battery (so it doesn’t just splash around and on the top of the battery and evaporate), so my advice is to moisten the adhesive with plenty of solvent.
This cable was pretty hard to remove at first. I had to gently wiggle it from side-to-side in the socket before it would let go.