With this sort of thing is it just gain/compression/signal strength going into the pedals & amp that's affected, or would there be a noticeable drop in volume when switching to the neck pickup from the humbucker?
My suspicion would be a noticeable volume drop between neck & bridge pickups. I may be wrong. You'll have to play around with pickup heights. One concern would be that lowering the bridge to balance volume with the neck, might cause the bridge to sound a bit anaemic.

That said, there is such a thing as a "volume control" on the guitar.
Apparently it somehow controls volume