I think, upon electrification, some electric intercity services should be made first stop Bedford, while the connect services can be extended to Leicester calling at all stations from Bedford. Corby will then be served by extending Thameslink Bedford services (this was an early ambition - the announcements on Class 700 contains Corby).
So, that means:
Intercity - Sheffield: St Pancras, Leicester, current pattern (no change)
Intercity - Nottingham: St Pancras, Bedford, Kettering, Leicester, current pattern
Connect - Leicester: St Pancras, St Albans, Luton Airport PW, Luton, Bedford, all stations to Leicester