My thought - more generally, not just Thameslink - is that, within 'TfL land', then TfL should be specifying services and fares; outwith that area then it's National Rail/GBR. For some lines/areas//service groups (e.g perhaps out from Euston) then it is relatively easy to have two separate Operating Companies, with separate contracts. For others - such as Thameslink - it will be more difficult - so I would suggest is more of a three way contract with TfL saying within our area these services, these fares; and beyond GBR/whoever those services, those fares; and the Thameslink Operating Company agreeing to provide them - and ensuring, as part of the negotiations, that the practicalities of changing service requirements when the boundary is in the middle of nowhere get sorted out.
And from the passengers' point of view, their trains will just change from TfL to GBR services (and back again) - but be the same trains...