I like the idea of the boost only transformer and letting the VD take up the extra. It is within my comfort zone, meaning even if hokey my opinion would be it's legal and safe. Supply nameplate voltage at the motor terminals, +- 10% of nameplate is usually OK, with max efficiency right at nameplate
Since it's non standard I would spell it out in writing to the owner and have him sign off on it as a money saving variance. I would say he has to give informed consent, then I would not worry about it coming back to me years later.
As Jon says, typical autotransformer boost only carries a fraction of the kVA for sizing the transformer. Typical secondaries are 12 / 24 and 16 / 32, so the 32 V boost at 12 A is 384 VA or a .5 kVA autotransformer. I have a basement full of those, I save the takeouts.
Autotransformer could be either end but boosting at the service end would have a higher Voltage and less current through the run length (marginally), while boosting at the load side, autotransformer could easily be after the pressure switch saving the idle winding heating (also very marginal). Probably a wash unless the run time is a lot, then boost the service side.
The no egc, I don't see a way around 250.4 (3). Only exception I could see would be entirely non conductive enclosure apparatus /equipment, no exposed metal, which I assume does not apply. It has to have an egc afaik.
System reliability and reduced repairs over the long term is a key factor. Any downtime for service and repairs will quickly eat up any savings from the various install methods. The drive would be fragile in that regard. The autotransformer would be indestructible.
That type of run, I believe they make a product the conductor is already in the pipe on a reel.