In almost any case the battery will be bloated when it's "dead". Opening the other side and pushing the battery with a 8-10 mm screw was the solution for me. The risk of puncturing the battery is less than when pressing with a screwdriver. Be careful not to damage the ribbon cable that runs across the battery.
JBL could have used standard-18650 cells instead - cheaper, higher capacity, and much easier to replace, but they prefer to sell us a new, incompatible (when it comes to pairing two of them) speaker. Shame on you, JBL :-(.
