OWC, also a reputable source of Mac stuff, sells a replacement battery and has a video showing how to remove the old one and install the new one (https://eshop.macsales.com/item/NewerTec...). At the beginning of the video the viewer is warned that the battery will have to be calibrated for best results, that the procedure will be demonstrated at the end of the video, and it should not be skipped. Basically, the procedure involves charging the battery until it is full, completely discharging it, then recharging it. I suspect the calibration might apply to the iFixit replacement battery as well.
Regarding that battery and a report that it doesn't work for OS X 10.11.2: What about later versions? I have 10.11.6.