Most compressor controls that I deal with use a timer for the unloader circuit. The motor runs for the time set on the TDR, without compressing any air. You can definately hear the difference when it times out. A pressure switch with a deadband or differential setting wouldn't require the use of an aux N.O. contact. Using 2, open on pressure rise, switches, would require use of one aux. N.O. contact to seal in across the lower setting switch until the higher pressure setting switch opens. Alternators usually use one aux N.O. contact from each contactor, in parallel, to alternate when the compressor stops. The minimal components that you describe don't seem to be enough for a dual compressor ladder.
Joe