(No bioengineering background here though, so what do I know.)
I'm not sure this is a good goal to have. To paraphrase Jobs in his Stanford Convocation speech, death allows the clearing of old ideas and provides urgency to motivate the living. Further, the infinite-living "you" would no longer really be "you", since all the matter and its organisation would be replaced several times over. (Biologically, this also happens but at a different scale so the organisation is more preserved). Arguably, your own ideas, thoughts, and concept of self remain.
I find the idea that an infinite living "me" would not be "me" very strange. It's like saying that if you keep adding fuel to a fire, once the original fuel has burned away it's no longer the same fire. My mind is a dynamic process, even if it changes state, it's still a continuation of the same process.
Ultimately, the ideas and urgency of ordinary human beings probably won't determine what happens to humanity in the long run. We're on course to develop powerful AI even with the technology and ideas we already have. Who knows what will happen then, but I think a stagnated immortal human race is a very unlikely outcome.