This may or may not work and only testing on the board will prove;

Your implementation has a momentary button that grounds an input line which in turn selects a sound file, and the pwrbtn is left unconnected? If so, this provides an always on, momentary audio output.

In the adafruit adaptation, the device is powered up via a capacitive link from source power to the pwrbtn input. Without further driving of the pwrbtn input, the device is always on until removal of power. As indicated in the data sheet, a high signal of 2 secs on pwrbtn will sudsequently shut the device off. As you've identified, an 'activity' signal provides a low on sound, and a high when complete. It would then follow logic that the high on completion could be applied to pwrbtn, turning the device off. That would further follow then that a momentary pulse on pwrbtn be required to turn the device back on. Your current momentary button must remain, to choose a sound file, yet prevent looping.

Here is what I would try. Replace your momentary with a double pole single acting push button, if it isn't already. One pole will remain as is, select input pulled low through a normally open contact, the other pole pulling pwrbtn high via a 10k resistor to Vdd through a normally open contact. Connect 'activity' output to pwrbtn via a 10k resistor. Check for operation.

 

Here's my take on a circuit to do what you want.
When the PB is pushed, it will turn on Q2 and power the circuit.
When the Activity signal goes high, it turns off the power.
Q1 and Q3 are needed because of the undefined state of the Activity pin when the Sound Board is not powered.

View attachment 100778

Hi Crutshow, I had a go at the circuit you made. Unfortunately it didn't work. The boards power led and activity led just kept pulsing and making a jitty noise.

 

Try connecting a 1-10 ohm resistor is series with the switch and then a 1000μF capacitor to ground (from Q1 collector).