The cable run is on a hillside of mostly sand and gravel soil, not sure what the soils magnetic properties could be.
We have run a #2 AWG 3 conductor ACWU aluminum armoured cable using 2 conductors for the 600V and the other #2 conductor along with the bonding conductor and armour in the cable grounded. We have grounding electrode on the 120/240V incoming utility service and another electrode at the load end on the load side neutral of the transformer.

The no load losses due to inductive or capacitive cable properties at 600V
would seem very small in my opinion but that is something we have yet to
measure. I recognize there are significant losses at utility distribution voltages as you mention especially cables of larger size.

We know that the utility will not be metering reactive power in the system but we believe there would have to be reactive power especially in the higher impedence of the lightly loaded 600V windings and I wonder what effect this has on the core efficiencies of the transformer.

It would seem to me that having the voltage and current out of phase like this must have some effect on transformer efficiency but adding a capacitor somewhere would consume some wattage too.