So for those looking for a battery replacement for the Big Blue Party speaker, I ordered one from http://xpresstekstore.com/7000mah-high-c...
The installation for this battery is easy: remove bottom screws, unplug the battery pack and replace. Tip: I unscrewed the small circuit board that the battery pack is plugged into (5 small screws), just to make it easier to unplug and plug in the replacement. Reinstall the bottom and you are good to go.
I've run this new battery pack through a couple of cycles so far and, as advertised, it has a much longer charge than the original battery pack from Brookstone. Highly recommended.
Thanks to Alex P for his good customer service at xpresstek.