On Re-assembly, I found this to be the hardest part. I resorted to using the provided tweezers and taking turns left and right, working it back into its ZIF socket. If someone knows a better way, please share.
Tip: when testing the battery's fit, once you have it in place and the screw holes are lined up, I made two little marks with a pen right where it tucks under the screw posts. Then once you have the adhesive backs removed, just hold the battery upright and line up with your markings, then tilt it down and tuck it under.
My speaker wire was wedged under the edge of the battery. I proceeded to step 35 and removed the two battery screws. This freed up the cable.
On my MBP there was an adhesive holding the speakers down. So, "lifting" was not exactly accurate.