that sounds incredible! glad to heat that it had worked for you.. googling "solenoid" doesn't make me all too smart. you possibly have a picture (or link) of the particular part that you used?
I did not make it.
A clarinet already has pads to cover the holes so an ordinary solenoid to press the keys was all that was required i think.
You need about 10 litres per min at about 1 psi i guess.
Looking around that's fairly tricky to achieve, most sample pumps are diaphragm and .5 l/s.
I have similar to one of these
If you can afford, they are very hard to come by second hand but i was lucky, old dentists surgery.
A fair few people have hacked refrigerator motors for airbrushing and they are very quiet so that is probably your best bet.
It's probably best to get the air supply sorted before you waste time on the rest.
Best i could suggest from new would be a diaphragm airbrush compressor and a bellows with a weight on to take out the pulses.
possibly using a gas low pressure regulator.