This sounds like it could be a perfect route for the proposed Alliance Rail “GNER” open access operation, as well as their other planned routes.
Though, if it did ever happen, and became anything more than an aspiration, which I quite doubt anyway, and it went to a franchised operator, I would imagine it would go to East Coast, not EMT. No chance of Grantham to Nottingham being electrified, the service would undoubtedly use HSTs: Assuming a two hourly service frequency, coinciding with the London-Newark path of the pruned KX-Lincoln service proposed under Eureka, the service could just about be run with two HSTs, assuming a journey time each way of around 1hr 45mins, which with some fiddling of East Coasts’ HST “fill in” diagrams to Leeds and Newcastle during the day might be plausible with their current fleet.
It would be difficult to increase the speed to 125mph over large distances at the south end of the MML, as the EMT services need to be pathed through the slower Thameslink services that have more frequent stops, EMT have cited this as an issue with reducing journey times in the past. Although there is plenty of four tracking at this end of the route that must counteract some of these difficulties. And with the “wiggly” nature of the route, in other areas the only way to speed up line speeds would be with realignment of various corners, and possibly constructing “cut-off” sections to some of the tighter bends.
The biggest benefit to journey time that can be created on the MML is through employing trains with the fastest possible acceleration, as opposed to the highest possible speed, and the Meridians are ably suited to quick accelerations. It’s the reason that HSTs were deployed to the route (As well as to raise the image of the Midland Main Line): Not because of their 125mph top speed, but because with 4,500hp and only 8 carriages, they are a lot quicker off the mark than a class 45 and mark ones.