I still suspect that your distinction between cyclical and linear time doesn’t make much of a distance in this case. Why couldn’t the transhumanist agree that time or at least natural processes are ultimately cyclical, in which case our species will eventually be extinguished and replaced by another one? What the transhumanist would insist on is that the end of our cycle amounts to our godhood via technological progress.
Progress is possible in a cycle as long as the progress is stipulated to be relative rather than absolute. Whether time is subjective or objective, as long as some events come after others, the transhumanist would want to say only that we’re headed toward techno-godhood. Now that future point may count as the end of our cycle and the beginning of a posthuman species. Alternatively, the definition of cycles might be arbitrary and pragmatic. Is it obvious and objective where one cycle begins and another ends? Either way, the transhumanist’s point about progress doesn’t seem threatened by your distinction.