I haven't seen it (except for the very first video), but how do rejuvenating blood transfusions qualify as "staying within the grounds of what is realistically possible"? And for that matter, why is "trait positiveness" gender-locked?
The trait positive blood itself was given a Hand WaveTechnobabble explanation involving a specific type of ribozyme. It has limitations as well; it can only extend a life for about fifty years longer. No trait positive males have appeared in the series, but that's not to say they don't exist. Male trait positives would probably not be so easy to identify or obtain, given that the Hymn of One especially values females, so it makes sense to them that "special" girls are selected to be raised in protected homes and given unusual diets and teachings.
There is such a thing as sex-linked characteristics. Maybe the Y chromosome inhibits the trait from being expressed.
In the July 14th live chat, The Creators confirmed that the trait is genetically linked to girls.
Which is fridge logic if you know how sex linked traits work, since the X chromosome carries the traits (the Y doesn't do anything but change ones gender), boys would get the trait as much as girls if it's sex linked, it would only matter when applying to whether girls get the trait from the mother or both the mother and father since boys will have the trait pronounced or not regardless if it's dominant or recessive. A sex linked trait only means it is passed on through the X chromosome, and the father only passes the X chromosome to the daughter, the mother passes on the X chromosome to either gendered offspring. This is basic high school biology.
That is not how sex-linked traits work. Sex-linked traits are defined as traits carried on one or the other sex-chromosome. Y-linked traits will never express in females, but X-linked traits could (and usually do, though to a lesser extent) express in males. The more accurate explanation would be that the trait in question only expresses in XX pairings, which is also possible.
...which has since been retconned by the LG15: the resistance finale, which does feature a trait positive male, but states that they are very rare.