If the 2 track section is such a bottle neck some of the paths should go via Corby. Its a wasted line.
It's a line not used much by passenger trains, but that doesn't mean we should start filling it with such just to justify it.
At the moment, it takes over an hour and a half for a regular EMT service to do Derby - Corby - Kettering (e.g.
http://www.realtimetrains.co.uk/train/C67069/2018/10/10/advanced).
Running Derby - Leicester - Kettering takes around fifty minutes (e.g.
http://www.realtimetrains.co.uk/train/C69924/2018/10/10/advanced), almost half the time of the Corby diversion.
Plus the Derby - Corby - Kettering service (whilst being overtaken by a few other trains between East Midlands Parkway and Kettering) avoids the city of Leicester, so diverting longer distance trains via Corby is significantly slower and manages not to serve the biggest intermediate place on the line.
Maybe there's a market for some Corby - Loughborough - Derby/Nottingham services, but I'd see those as being shuttles run by Sprinters rather than delaying long distance services with that diversion.
Two fast (i.e non-stop) and two 'slow' (i.e. Bedford, Wellingborough, Kettering etc) an hour to Leicester, on an even-interval 30-min service for each, would have been adequate I'd have thought: indeed what was wrong with the old system of the 'fasts' overtaking the 'slows' with connections available at Leicester (thus providing one direct train and one with-change an hour to each of Sheffield and Nottingham)? That old timetable always seemed very 'neat' compared to the rather messy current timetable; the only issue that springs to mind was that a 170, or even a 4-or-5-car 222, was too short
If the MML only served one of Derby/ Nottingham (e.g. if Derby was served by a rebuilt GCR or Nottingham served by ECML services turning off at Grantham) then I could get behind the idea of two fasts and two slow from London to Leicester. It'd be nice and neat.
But now that both Derby and Nottingham have two relatively fast London services per hour, to return them to the days of just one fast service (with a second service so slow that it is almost overtaken en route), which I'd see as very unpopular.
Other cities a comparable distance from London (to Derby/ Nottingham/ Sheffield) have a fairly uniform London service (Norwich, Leeds, Manchester, Birmingham, Bristol etc), rather than one ultra-fast service and one stopper.
EMT's biggest success on the MML seems to be the smoothing out of the times for long distance services, even if that means slowing down the "fast" train slightly to give more like a half hourly service (when the second Sheffield service started, it often left at xx:35, just eight minutes after the traditional departure for London).
If you could amend the timetable to permit six Leicester services per hour then that would permit all longer distance services to be non stop as far as Leicester, allowing faster journeys for passengers who are on the train longest.
Personally, I don't think that demand from any station south of Leicester is significant enough for through services to places north of Leicester to be necessary - fine if operationally practical but there's demand spread between six stations (Airport, Luton, Bedford, Wellingborough, Ketting, Market Harborough) and it's not practical (for longer distance trains) to serve them all.
But, Thameslink is the bigger priority, which is why we have such awkwardly timed MML services for passengers travelling north of Bedford.