Does your speaker still power on when it is running on battery? If it does, you can bypass factory charging circuitry and make your own charging port. I did this on another speaker, but it should work on Big Blue just the same.

Here are some basic guidelines:

I used 2.1 mm x 5.5 mm jack

Ex:.https://www.mouser.com/ProductDetail/Swi...

Solder two wires to the jack. Red in the center, black to the ground lug.

Drill a hole in the housing where it won’t interfere with anything, install the jack.

Connect wires from the jack to the battery wires. You will need to do some splicing here, but it is basic red to red, black to black.

Get a 12.6V battery charger, 1A or 2A will do,

Ex: https://www.ebay.com/itm/12-6V-DC-2A-Bat...

Use the charger to charge your battery through your new jack. Less than $10 and 1 hour of work.

Update the guide with battery description and connector information. Hopefully this is enough to point you to the right direction.

Remove front button bezel and the rear panel, there is a grounding wire soldered to the screen in the battery compartment, just cut that. then it should just slide off.