Wayback in the 70s, I had a small 2HP electric air compressor that I wanted to convert to gas engine power. This pump was nothing like a Quincy, just a 2-cylinder, single stage pump (reed valves in the head).
The parts were available from Campbell Hausfeld, consisting of 2 pneumatic control valves, and I believe they were referred to as an unloader, and a governor (no connection to the engine throttle). I got a new Techumseh 5HP engine (Small Engine Distributors, in the midwest USA) to replace the 2HP electric.
I don't think the idea was to vent the pump's full displacement air to atmosphere, but it did prevent the tank pressure from increasing until the tank pressure dropped to a point where it needed to be increased. It made a lot of hissing noise out of two small (maybe 1/8" ports), so maybe it was venting the pump air.
A Quincy distributor/parts dealer should be able to provide the correct parts to ensure that the setup is safe and operates efficiently.