After discovering he’s genetically incapable of love, a cautious soon-to-be dad must race to California for an underground gene therapy procedure before he’s thwarted by the Department of Bioethics.

I would reverse the premise.
He has the capability to love in a society that condemns emotions.
The arrival of his child just elicit more emotions in him, which will make him a suspect.
He therefore has to find a way to suppress those emotions.
He cares, so he has to hide it.
Will his love for his child push him to stop loving?
To me that makes more sense and you can keep the same bioethics, chase and emotional moments.
Equilibrium on a similar concept went the action movie rather than psychological and drama.

I understand the story to be, a man who thought he was incapable of love and blamed his genes but discovers in the underground that he was capable of love all along. A journey of discovery. Or, he is an experiment of the Department of Bioethics and he was not supposed to find out that he has this problem, and becoming a Dad has just brought it to his attention. Is this a comedy?

Good point.