Genuine question, why is it not up to the owner of St Pancras to fund capacity enhancements at their station?
You could just have a quota for the number of passengers to board at St Pancras, with the rest reserved for Stratford, Ebbsfleet or Ashford.
It's fair to say most passengers want London, but Stratford is basically East London's Clapham, with very different connections to the Eastern side of London (including Canary Wharf) and Eastern Home Counties. Often, Greater Anglia leaves Liverpool Street half full (if that) and fills up at Stratford. Yes, many Anglia pax want the Olympic Park and Westfield and HS1 pax hardly will, but most cross-Channel passengers live in the suburbs of London and Île-de-France, not Central London, especially if fares become more affordable.
And if East Londoners are willing to travel to City, Southend and Stansted Airports, let alone Heathrow, I don't see why Stratford wouldn't be a success.