I got a set of horns from a salvage yard with the same set-up as yours. I don't know if they are Hadley brand, but the vacuum pump and the tank look exactly the same. Although my pump did work off of vacuum pressure, I could never get enough pressure out of it to blow the horns. I tried for a long time, but I think the diaphragm was too brittle or something. My horns also had mud-dauber nests in them that needed cleaning out. You're right - if they work, no need to take them apart.
I used the tank, horns and electric solenoid and added a 12v compressor with a pressure switch to turn it on/off.
And you are right - those horns are LOUD!
Good luck with yours.
Craig