I think you meant to say transhumanism would NOT further our connection to God, right? Yes, that would be a traditional Christian reading of the matter. And yes, Christians are free to say that organized religions are bound to misinterpret or to stray from their founder's vision. The question, then, is whether the organization is still a useful vehicle for spiritual purposes. Moreover, the institutional betrayal can become so egregious that spiritual seekers can no longer associate with the religion without disgracing themselves.
I agree that technological progress isn't the same as a moral or philosophical kind. Still, technological revolutions often force the issue, changing the environment to which we must adapt.
By the way, the "diabolical mimicry" point is more revealing than it seems in your use of it. Justin's Martyr's point was that the pre-Christian myths of the dying and rising savior gods were diabolical mimicries because they were miraculous in coming before Jesus. The demons foresaw that Jesus would come so they muddied the waters in advance. This means that early Christians conceded that there was such a pre-Christian mythos out of which Christianity might have naturally evolved.