Thanks you very much for your clearly well considered answers!
The MDBT42 module sounds great, what functionality might it have out of the box?
Setting the name to blank works perfectly well for my purposes.
Final question (I promise): From this answer I can see that it's possible to hook a wifi module into the puck, but it would have different power requirements. IRC, the highest sensible voltage for the puck would 3.7v. If I used something like this to power the puck + wifi module, would that be sufficient? Would the Puck still be able to sense its battery cap?
Apologies if I'm rambling. These questions are coming to me as I type.