Finally, it is all back together and now working.

Some changes I had to make:

• USB power bank PCB. There was an issue with the USB power bank I selected in that it would not support the instantaneous power draw of the speaker powering up. Why, I don't know, as I gave the DC-DC a long time to stabilise before powering up the speaker. The solution for this was to use a different power bank PCB from an old power bank l had. This powered the speaker up fine with no problem, even using minimal capacitance and long leads.
• Speaker power-on. For some reason (and I was losing patience by now) the speaker would shut down 1-2 seconds after powering on. It did not look like a voltage issue or a relay bounce issue and it only seemed to happen every 10 power-ups or so. Again I don't think it was related to voltage as it did it even powered from a PSU. It may have been to noise from the BT module I suppose. The solution to this was to find a spot on the PCB that was over about 3v during power-on so I could retry the power-on. After a bit of faff I found one and soldered some resistors and a pulldown on there to get a signal. To avoid any new layout or connectors I used the ICSPDAT and ICSPCLK on the PIC - the ICSP I simply used as a ground (setting to output and low on powerup) and the ICSPDAT was the clock. A small adjustment to the software ensured that the power up was retried as many times as necessary.