If you swapped the East Coast Inverness service onto a different hour's departure from Edinbrough to Kings Cross (can't remember which one, it currently comes through from Aberdeen) I think you can run the Sleepers and East Coast's Scottish drags with 5 locos (assuming they don't brake down).
In England, I think East Coast's services would require 4 locos for dragging. If you add Grand Central's Sunderland service, I think you need another 2 locos. Finally, I think the rest of the Open Access service on East Coast (Hull Trains and GC's Bradford trains) would add another 4 locos to the requirment.
In total, that's:
- Scot Rail sleepers and East Coast services only - 9 class 67s
- Above plus Grand Central Sunderland service - 11 class 67s
- Above plus Hull Trains and Grand Central to Bradford - 15 class 67s
15 existing locomotives working mostly away from the wires has to be cheaper and more enviromentally friendly than putting 35 5-car IEP bi-modes on East Coast. Given that East Coast only have eight off-wire services each way, those 35 sets are going to spend alot of time sitting uselessly in sidings or running under the wires.
Chiltern currently have 5 mark 3 sets I believe. If they never require more than 10 locos in service a day (more than double current arangments, since 1 of the 5 sets is apparently being refurbished) then there are 5 spare locos to replace failures. Is 5 spares in a fleet of, I think, 30 locos enough? The 67s would have to be in a neutral livery of course, and the Fife circle would have to revert to multiple unit operation.