It seems like you are not framing NP-completeness properly. An NP complete problem is simply worst case hard. Such a problem can have many solvable instances. With some distributions of randomly selected SAT problem, most instances can be quickly solvable. SAT solving contests often involve hand-constructed SATs translated from other domains and the entrants similarly add methods for these "special cases". So NP-completeness isn't a barrier to SAT-solvers scaling by itself.