Forgive me if this is a foolish suggestion, but surely it wouldn't be impossible to swap the DVT and the 91 so that the DVT runs at the Scotland end and the 91 at the other end thereby making the loco swap easy?
Uh no, you would still have the issue of having to modify the loco used so it works with the DVT ie the WSMR Class 67s have had remote fire fighting equipment fitted so they can be operated by the DVTs although when replaced with other members of the Class 67 fleet, a driver does have to ride in the locomotive when propelling in case of emergency.
You would also have to modify the DVTs to work with the Class 67 by doing what WSMR has done which is adding a notched power controller as is used in the locomotive and a 27 wire jumper cable as used on the GM EMD locomotives which is known as the AAR Multiple Working system.
So because of the work to the WSMR DVTs, they have had to be renumbered although they can still work with TDM fitted electric locomotives.
With the East Coast sets, the Class 67 is always at the leading end and never propelling so even if they as in East Coast decided they would follow National Express East Anglia's example and have the Class 91 at the London end and the DVT at the Country end, they would still need to pay for the modifications to the DVTs and Class 67s which would be expensive if shunt release moves weren't used
No, far far easier just tackling a Class 67 onto the leading end of the train and have a second Class 67 couple up to it at it's destination, freeing up the 1st Class 67 to then shunt release the next working.
And seeing as there is not that many services from Aberdeen/Inverness to Kings Cross
07:52 Aberdeen to Kings Cross
09:52 Aberdeen to Kings Cross
14:50 Aberdeen to Kings Cross
17:37 Aberdeen Arrival from Kings Cross
21:12 Aberdeen Arrival from Kings Cross
07:55 Inverness to Kings Cross
20:08 Inverness Arrival from Kings Cross
Although the Aberdeen's might required some work planning the Class 67 moves, there really is no reason why the Inverness's cannot use the 91s DIT and have them dragged from Edinburgh to Inverness and back again seeing as there's about 5 hours between the two services at Edinburgh which is plenty of time to clean/refuel and have the loco standing by at Edinburgh during that period.