Obviously, giving the Welwyn and Hertford stopping trains (I believe Moorgate can just about get to 14tph instead of 12tph with the current signalling) to be London Overground, with the Welwyn and Hornsey (Inner) drivers taking over. I'd standardise the timetable at the same time, taking advantage of capacity to Stevenage now and what not.
There needs to be 4tph between Finsbury Park and Blackfriars on Thameslink off-peak, and 8tph at peak. The best way to achieve this is to operate the Peterborough and Cambridge services to Brighton, creating a standard 15-minutely path between Hitchin and Three Bridges. Bedford services can then go elsewhere (Reigate eventually, Horsham, Grinstead etc.).
To add a peak-time overlay, I'd smash in the Cambridge 'slow' (but amend it, so as to run it Cambridge - Foxton - Shepreth - Meldreth - Royston - Ashwell - Baldock - Letchworth - Hitchin - Stevenage - Knebworth - Welwyn North - Finsbury Park) and a Royston 'slow' (Royston - Ashwell - Baldock - Letchworth - Hitchin - Stevenage - Knebworth - Welwyn North - Welwyn Garden - Hatfield - Finsbury Park), both going south through Blackfriars to 'somewhere' (Gillingham via Herne Hill and Ashford Intl via Herne Hill make reasonable sense!). Off peak, it would just be a Cambridge - Kings Cross slow service - no through running.
That would leave the Kings Lynn and Peterborough express services unaccounted for, and the Welwyn peak 'special' services. See next.
The Kings Lynn services, which I estimate even if you use 8 car trains north of Cambridge, and even if they ran half-hourly, would require 26 units maximum, should be operated by 379s (we worked out in a previous thread there's a 30 second time penalty on the fast lines south of Hitchin in either direction maximum as a result), and be an LNER service. Train crew at Kings Lynn and Kings Cross for this. Light maintenance can be done at Hornsey or Bounds Green, with heavy work sub-contracted to Ilford as might be standard.
To finish, you require some IEPs (I believe there are some spare due to the timetables not quite coming up to full anytime soon) to do the peak Peterborough trains, which should omit the Stevenage call (those folk can board one of many other services, or put a call in on other Intercity services for connectivity), and be fast Kings Cross <> Biggleswade. They could be extended north of Peterborough to the Grantham 'back platform', Newark or even Lincoln at peak times. Train crew based at Peterborough, split with Thameslink. As some of the Kings Cross establishment would be needed for Kings Lynn work, you could use the Peterborough drivers for Lincoln, Newark and some stopping York and Leeds work to 'make up for it'. If you need some extra stock for Peterborough peak work, I would probably go so far as to have a fleet of 'plain' 387s which could be sub-leased from Southern during the Monday to Friday time, cycling on and off maintenance at weekends south of the river. It's a perfectly workable solution.
I'd also move the Hitchin driver depot to Letchworth, as so many units would be coming on/off there at the start and end of service.