How's about this. Let's assume demand for sleeper is generally increasing, and separate Glasgow and Edinburgh trains would be needed in future.
Euston keeps the Glasgow sleeper.
Edinburgh sleeper shifts to the ECML. All the infrastructure is in place to access this from St. Pancras. Sleeper then starts from Gare du Nord to St. Pancras as a late evening service - part cabins, part reclining seats. Train is effectively split in two with Paris-Edinburgh passengers in one half and Paris-London passengers in the other. At St. Pancras the London-bound passengers depart, the train is security-swept and London-Edinburgh passengers come on board (think a similar thing happens on the Amsterdam Eurostar at Brussels). The half hour this takes is not an issue as the sleeper isn't really time-dependent.
But ultimately does this have any advantage over changing from Eurostar to the existing sleeper service in London?