This might be aided by mastering the aging process. If medications or techniques are invented for drastically slowing down the aging process, say that a healthy person can live for a few hundreds years at least, I bet this would speed up the divergence of the species. Because likely those technologies will be expensive and reserved for those who can afford it or are part of "elite" circles, and also because if everyone could live that long then we would need to start having many less babies or the population would explode.
So the lower diverging branch will be producing most of the babies, and not have access to these technologies; their reproduction rate will continue to more or less balance out their death rate, while for the upper diverging branch they will have many less babies (but probably still some), in order that their own replacement rate will stay more or less the same over time too.
I cannot really see it happening any other way, unless all of humanity were given access to this technology and then everyone would stop having as many babies... but that is not going to happen. Certain parts of the world are very much baby-makers, compared to the west. Even if you gave age-overcoming technologies to the third world it would simply have even more babies than it has right now. I am not really concerned about overpopulation, it does not bother me much and I think children are pretty cool, however I would be bothered if everyone started living until age 300 and the same or even more babies were being born... logically that would lead to catastrophe and war in a very short time.
To live longer means more expense and technology are needed. That is fine, but it needs to balance out. And perhaps living that long is not really philosophically good anyway, or even living to 70 or 80. It would depend on the person... I think it was Nietzsche who said people should die at the right time. or something like that.
Age, living longer, is itself not an inherent value. This points out one of the central flaws with transhumanism. But I might not mind living for 300 years, it would depend on how I could live. If I knew that I had that much time I think it would change how I look at my life and what I do with it. But even if you live a long time, or perhaps indefinitely, it is still the case that your mind ages, your heart ages, and you come up against very severe ennui limits. That would be one of the most difficult parts of living so long, but maybe also a fun challenge. Assuming you had enough money to keep up a lifestyle conducive with pushing back the ennui barrier.