The EXO-001 is 20mA max, while the 45 draws around 35mA. You want either the 40mA version of the BCP-15, or a "Dowdy choke" for serious overkill! :^)
I would not go below 10uF for the final PSU capacitor, and generally I like this one to be the best and the largest. I know, I know, those are often mutually exclusive! You might want to breadboard the circuit before cutting metal so you can listen to options like these before committing.
Sounds like a fabulous project - please keep us all updated as it progresses!