Is it possible to just do the controls at Ashford (going to the continent) or Lille (going to the UK)? That is, for services to the continent, the reservation will only start at Ashford and passengers can take any HS1 trains adhering to the official connection time (the time needed for border control) there, with Eurostar trains acting as a local train between St Pancras and Ashford in addition to the Southeastern trains.
That is, for a continent-bound journey, a passenger takes any appropriate local services to Ashford, go through the border control there, and take the booked train to the continental destination, and in the reverse direction, takes any appropriate intra-Schengen services to Lille, go through the border control, and take the booked train to the UK destination which can carry local Ashford-London commuters if it stops at Ashford as well.