I will most likely post this again in a new thread in a few days with my changes to Southern, Great Northern, SWR, EMR and Southeastern also explained, but here is my idea for Thameslink.
Changes I have made:
The biggest change I have made is to convert the service north of the core to a 6tph base timetable instead of 4tph. This has many benefits, including that Brighton services can be equally spaced every 15 mins from the core southwards and still run to both Bedford and Cambridge, and skip-stopping services to Luton (currently the Rainham services) that provide additional services to some stations but skipping others will not be needed anymore, simplifying service patterns.
Sutton via Wimbledon services run into the Blackfriars bays, as these services are unnecessary anyway since the Northern Line to E&C is much faster than Thameslink from the Morden and Tooting areas.
My plan requires a new 12 coach Platform 3 at Reigate to be built.
New services run to West Croydon via Tulse Hill and Crystal Palace, providing new connectivity along the corridor of the 68/468/X68 bus routes which are very popular.
Services run all stations to both Welwyn and Hertford, with both lines having an equally spaced 4tph that alternates between Thameslink and Moorgate. Some platform extensions will be needed on these routes.
Service pattern (stations in core not shown as it would be repetitive):
Bedford to Brighton 2tph (12 coach)
(Flitwick, Harlington, Leagrave, Luton, Luton Airport Parkway, Harpenden, St Albans, Brent Cross, West Hampstead...London Bridge, East Croydon, Gatwick Airport, Haywards Heath, Wivelsfield, Burgess Hill, Hassocks, Preston Park)
Cambridge to Brighton 2tph (12 coach)
(Royston, Baldock, Letchworth, Hitchin, Stevenage, Finsbury Park...London Bridge, East Croydon, Horley, Gatwick Airport, Three Bridges, Balcombe, Haywards Heath, Burgess Hill)
Bedford to Horsham 2tph (12 coach)
(Flitwick, Harlington, Leagrave, Luton, Luton Airport Parkway, Harpenden, St Albans, Brent Cross, West Hampstead...London Bridge, Norwood Jct, East Croydon, Purley, Coulsdon South, Merstham, Redhill, Earlswood, Salfords, Horley, Gatwick Airport, Three Bridges, Crawley, Ifield, Littlehaven)
Bedford to Reigate 2tph (12 coach)
(Flitwick, Harlington, Leagrave, Luton, Luton Airport Parkway, Harpenden, St Albans, Brent Cross, West Hampstead...London Bridge, Norwood Jct, East Croydon, Purley, Coulsdon South, Merstham, Redhill)
St Albans to Sutton 2tph (8 coach)
(Radlett, Elstree & Borehamwood, Mill Hill Broadway, Hendon, Brent Cross, Cricklewood, West Hampstead, Kentish Town...E&C, Loughborough Jct, Herne Hill, Tulse Hill, Streatham, Mitcham Eastfields, Mitcham Jct, Hackbridge, Carshalton)
St Albans to West Croydon 4tph (8 coach)
(Radlett, Elstree & Borehamwood, Mill Hill Broadway, Hendon, Brent Cross, Cricklewood, West Hampstead, Kentish Town...E&C, Loughborough Jct, Herne Hill, Tulse Hill, West Norwood, Gipsy Hill, Crystal Palace, Norwood Jct)
Welwyn to Sevenoaks 2tph (8 coach)
(Hatfield, Welham Green, Brookmans Park, Potters Bar, Hadley Wood, New Barnet, Oakleigh Park, New Southgate, Alexandra Palace, Hornsey, Harringay, Finsbury Park...E&C, Denmark Hill, Peckham Rye, Nunhead, Crofton Park, Catford, Bellingham, Beckenham Hill, Ravensbourne, Shortlands, Bromley South, Bickley, St Mary Cray, Swanley, Eynsford, Shoreham, Otford, Bat & Ball)
Hertford North to Orpington 2tph (8 coach)
(Bayford, Cuffley, Crews Hill, Gordon Hill, Enfield Chase, Grange Park, Winchmore Hill, Palmers Green, Bowes Park, Alexandra Palace, Hornsey, Harringay, Finsbury Park...E&C, Denmark Hill, Peckham Rye, Nunhead, Crofton Park, Catford, Bellingham, Beckenham Hill, Ravensbourne, Shortlands, Bromley South, Bickley, Petts Wood)
Order of services and intervals between each service in the core (not the actual times):
00 Bedford to Brighton
05 Hertford to Orpington
07.5 St Albans to Sutton via Mitcham
10 Bedford to Horsham
15 Cambridge to Brighton
17.5 St Albans to West Croydon via Crystal Palace
20 Bedford to Reigate
25 Welwyn to Sevenoaks
27.5 St Albans to West Croydon via Crystal Palace
30 Bedford to Brighton
35 Hertford to Orpington
37.5 St Albans to Sutton via Mitcham
40 Bedford to Horsham
45 Cambridge to Brighton
47.5 St Albans to West Croydon via Crystal Palace
50 Bedford to Reigate
55 Welwyn to Sevenoaks
57.5 St Albans to West Croydon via Crystal Palace