I was getting about 20 minutes on a charge, so the battery obviously needed replacing. Ordered a kit from OWC. Got around to installing it tonight. If I hadn't forgotten to re-install a (non-critical) insulator, it would have been totally done in about 10 minutes. You can see the piece I originally left out in the upper right hand corner. Doh!
The online video warned about the problems with removing adhesive, but it was no big deal (2 small pieces of double stick tape). Here is the patient on the operating table, about to close up :