If I had the answer there would be no need to search for the new frame for the debate. There has been little or no philosophical work in this direction as conservatives and moral thinkers genereally have had their heads stuck in religious Holy Books and not in thinking about other reasons why hedonism is in itself morally incompatible with culture. Rand and the objectivists are probably among a select few that have went off in the direction needed to create a natural moral philosophy.
By the way, atheism necessarily leads to determinism as well. After all, in a Godless universe, everything is cause and effect. No free will.