Isn't it possible to design a compressor that can be started and stopped very frequently for capacity control? The motor and starting components will be designed for frequent starting (even with a pressure difference), and a pair of SCRs or a triac will be used to switch it on and off. There'll be a separate oil pump that runs whenever the unit is in use, to reduce wear on the bearings.
It'll switch on and off with a total period of 40 seconds or so.

I see my idea as a cheaper alternative to VFDs. In fact, about the only changes that must be made to a normal compressor are the motor, possibly the bearings, and the addition of a separate oil pump motor.