But this is impossible!  The type system of Haskell can be
handled by a Hindley-Milner-Damas style type checker.  Such a
type checker always comes to a halt with a Yea or Nay answer.  So
one cannot get a simulation of the combinators S, K, I inside the
Haskell type system.

What have I misunderstood?  And, in case GHC really does now
handle stuff beyond the HMD horizon, what does the New Core
language look like?