Then they either spend a fortune rewiring their entire mk.3 fleet for Power Car use or spend a fortune re-engineering the power cars to supply the Chiltern Mk.3's, severely doubt that will happen.
Actually you wouldn't have to re-engineer the power cars.
You could just stuff (almost) off the shelf static converters into the redundant luggage compartments of the power cars. (If a true SMPS is too pricey then a more bulky but simpler installation out of a three phase transformer and a six pulse diode rectifier would easily suffice).
Very little work to the PCs - and a new set of jumper heads would allow the AAR cables to function as HST MU cables - while the HST connector has 36 lines to the AAR's 27 only 24 of the former are actually used.
So assuming its a compliant AAR installation (all wires must be through wired on all stock) it should be fine to fit.
This is not the 1970s when the only practical means to convert between loco hauled DC/AC single phase and the three phase used by COTS equipment (like air conditioning units) was a motor-generator.
This is not even the early 2000s when the SMPS had not yet come of age (and the loco hauled Mark 3s had to be fitted with MU cables regardless) - this is now.