I think the poster meant that the diesel loco connected at the front (northern end) of a northbound train would provide the traction for these sections, with the pushing electric dropped at Waverley. In this scenario, the diesel would of course have to be powerful enough to propel the train to the required maximum speeds now used by the HST along these extension/branch lines (110? even 125?).
Also, for a return from, say Aberdeen southwards, the southern end of the train would have to have a DVT (as the first coach after the pushing Class 91) even in the original configuration leaving London in order to steer the now southbound train with the diesel pushing. Or alternately, a new pulling diesel unit is connected to the southern end when leaving Aberdeen, to be changed to a pulling electric Class 91 at Waverley. Which of course would again push when leaving KGX for the north...
So, extensive stabling and servicing facilities for Class 43s in the Edinburgh area required then (with the London area ECML HST depot downsized in unit numbers for peak/emergency use only). Which I assume would exist anyway?