There appear to be 2tph from St Pancras to Corby. Why not simply divert one of those to Leicester once electrified? Doesn't have to be both. The second one, if it's felt necessary, could be a shuttle back to Kettering to connect with the one back from Leicester or one of the ICs, sort-of-a-la-Windermere.
This was going to be my suggestion exactly.
People have been talking about "
the" MML problem, eg speed and/or lack of a fast platform at Bedford on the up - I'd say both a part of the problem, sure. But the other 'speciality' of the MML as it is now is that the Corby tail is wagging the MML dog.
Having re-opened Corby (very good!),and then decided on electrification of the MML (very good!), the powers at be could not leave Corby as a diesel island (understandably). So they began electrification but then stopped it at Corby (very bad for almost everyone bar Corby-ites, and MML long distance passengers who don't want the intermediate stations).
This thread has been comparing the MML with the ECML, WCML and even to Bedwyn - but while some comparisons are valid, each line has its unique characteristics. And on the MML one of those is the number and size of towns on the line twixt Leicester and London - a whole string of them which are neither monster traffic generators (at least if you discount London traffic) but nor are they dismissive numbers (as per, say, Arelsey-Biggleswade-Sandy-St Neots on the outer suburbans of the ECML for traffic heading north). Towns which, historically, at least for as long as most remember, have been well connected by a service that has been considered Inter-City standard (of the day) and typically fed into a fast Derby/Nottingham - Chesterfield-Sheffield at Leicester.
The Corby 'tail' is now wagging and broken that traditional linkage, bar a couple of very early morning services and Sunday mornings.