One cheap trick that can work if each module has a switch that is either on or off. It will not work for those with a single button that is only closed when pressed. Just get a multi-pole switch and use a separate pole for each module. then different voltages and polarities will not matter at all, and not much chance of ground loops either.

 

All you need to do is power the BT board from the 12V of the amp board after the switch. It should easily be able to handle the additional current for the BT board since it is capable of operating at twice the 12V you are using which would be way ore extra current than the BT board would use.

Bob