A possibility for MML traffic that occurred to me would have been to keep the Bedford-Hitchin link (closed in 1964, I think) and run the passenger traffic into Kings Cross that way.
I doubt that would have been considered at all. King's Cross was already going to be taking extra trains from Sheffield (via Retford) and Nottingham (via Grantham), so would not have had capacity for the Derby-Loughborough-Leicester service.
Anyway, by the time this was being considered, the line had already been largely dismantled.
The Leicester-Rugby (via Ullesthorpe) line had also recently been dismantled, but I think was considered for rebuilding. Even if it had been intact, it would have required a complete rebuild to take fast passenger trains, as the line had been a backwater for the previous 100 years and the track was in 'worn' condition. However, this line had a level crossing across the busy A5 trunk road (near the present Magna Park warehouses), which would have required a bridge building if the line was to be reinstated.
Both lines had awkward junctions with the main line at the southern end with a flat crossing. At Rugby in particular this was a slow turnout across all the up lines with not any chance of improvement. At Hitchin the Midland train would have to make a southbound flat crossing of the ECML, as well as northbound Cambridge trains.
In those days Leicester only effectively had one train per hour to London, plus one per hour that stopped at the intermediate stations to Bedford, Luton and St Albans. I guess an hourly DMU would have taken up this traffic, connecting with the London train at Market Harborough. Euston would only have had to cope with one extra train per hour, King's Cross two [and either of these may only have got a direct train every two hours?] However the existing WCML & ECML frequencies were much lower than today, both main line and suburban.