It would be simpler to have the air nozzle in the exhaust manifold and push directly on the impeller of the turbo. I would suggest an electric air compressor to eliminate air bottle filling.

There is a rumor that Nissan is going to be using electrically assisted turbos on the next GT-R. Essentially electric motors in the turbos speed them up in spooling when there is a rapid increase in throttle pedal angle detected by the drive-by-wire. No complicated auxiliary compressors needed.