with vast, expensive, works it would be possible to re-route the Long Distance through the disused bore of Copenhagen tunnels, and the suburban through the tunnel currently used by the fasts. Belle Isle would then need to be re-configured/rebuilt with an additional flyover,
If you were to get a seriously big budget together you could even go for running it as a six track railway to Finsbury Park, becoming an eight track railway there (with a rebuilt station) and cross platform transfer between Thameslink and the NCL, with the Thameslink tracks finally joining Slows and the GN suburbans the Fasts at Alexandra Palace. This would allow greater separation of the four service groups (Long Distance IC, Cambridge Fast & Peak Time GN, Thameslink and Moorgate) on approach to the core/their terminals providing a buffer to help with perturbations to schedules.