(a 20 HP idler is consuming quite a bit of juice!), it is not very economical in the grand scheme of things.
Not really...
An idling phase converter has a very poor power factor. That is to say the majority of the input current is out of phase with voltage. Thus, a much lower power draw than would otherwise be the case based on a current measurement alone.
The only power being used is that consumed by the bearings and magnetizing power due to core loss, electrical resistance, etc. For a properly balanced 40HP rotary converter that's around a kilowatt more or less. So, idling a converter capable of starting a 20HP motor for 8 hours will cost about $0.88
It is also possible to build a circuit which will start and stop the converter with the compressor, but that's too complicated to get into here. The VFD is also a good solution, especially if the OP has no plans for other 3-phase equipment.
All of this is predicated on the OP having a sufficient incoming service (and transformer) to supply the required power. Residential services, as a rule, employ heavily undersized transformers.