All energy regulatory bodies need to learn how to read a pump curve.  As LionelHutz said, "energy savings guides showing VFD's as automatic energy savers are "stupid"", and so are the people who believe them.  And a pressure-reducing valve is not going to add any detectable heat to the water, or have any appreciable energy loss compared to a VFD.
"Its just your normal type of domestic shower, except with a flow rate from really nice and powerful , to less so."
I think this means you have a pressure switch controlling the pump.  It will go from "nice and powerful" to "less so" as the pump starts and stops.  I think this also means your pump is plenty large enough for the shower.  You just need a way to keep the pump running and the pressure steady.  Backpressure or reduced flow from a pump control valve will do this, and also reduces the energy consumption of the pump very similar to a VFD.  A pump control valve will also work with a single phase motor, which you will have to change to a three phase motor to work with a VFD.

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