The way I read Brian, the Stoics don´t have the resource on their own to forbid abortion based on their philosophy, since based on solely that reasonably the question could be asked if an abortion due to disease or genetic disorders wouldn´t be the more mercyful action. I´m not open to that discussion, period.
Historically, that is correct. Seneca openly celebrates the father who leaves the disabled newborn to die, and he does so, at least seemingly, based on the Stoic conception of natural law. I'm not well-versed enough in natural law to say anything about how Stoic natural law differs from something like Thomist/Catholic natural law, although it would be interesting to flesh out the differences. I would think it comes down to what the natural activity and telos of the human being is conceived to be. For the Stoic it is merely reason (which includes all of the virtues as species of reason), while I think the Catholic would ascribe broader essential activity to the human being. For example, love would seem to be something a human being naturally and essentially does, that is not merely a species of reason/reasoning.
The Stoics have two types of natural law.
Stoicism has a sort of pantheistic understanding of the natural order. God isn't utterly transcendent but intimately a part of the cosmos.
"The universe itself is God and the universal outpouring of its soul; it is this same world's guiding principle, operating in mind and reason."
--Chrysippus, De Natura Deorum
God is an active intelligence, a directing flow. The movement of the cosmos is churned by Fate, a guiding divine intelligence. Seneca equates God with the providential nature of divine reason. So, in part, the Stoic natural law includes a conforming of our internal state to the divine intelligence, that is, an acceptance of Fate, its array of externals, and the subsequent balancing of one's internal mental state with the ebb and flow of the cosmos. This is roughly similar to the Thomistic metaphysical understanding of God as the the divine intelligence that directs all things towards their ends. Final causality is ultimately rooted in the divine and, without this intelligence, there would be no motion. Of course the striking difference is that Thomism views God as radically transcendent vis-a-vis Him being pure actuality.
The Stoics also overlap with Thomism with regards to the idea that each thing has an ordained nature. Thus a 'good' tree lives in accord with its nature, absorbing water, growing branches, taking in sunlight, producing buds, etc. However, it seems that the Stoics put more emphasis on the former understanding of nature as divine fate, hence the Stoic emphasis of coming to accept externals as the means to peace or apatheia. Whereas the Thomist would put more emphasis on the latter understanding of nature as an obligation to our ordained quiddity.
Thomistic natural law involves the agent coming to a greater understanding of his nature and then directing his will towards the proper ends of that nature. Stoic natural law, from what I understand, involves the agent coming to a greater understanding of the external affairs or Fate of the entire cosmic scheme and his place in it and then conforming his will to be in accord with it.
I can see why the Stoics would be proponents of euthanasia, seeing it as boldly accepting nature as divine Fate. And obviously the Thomist would be against this, seeing any deliberate frustration of a natural end as wrong (of course excessively cleaning one's ears, picking one's nose, could be classified as frustrating the end of those organs, however, the severity of frustrating those ends doesn't involve a rapid corruption of what it means to be a rational animal--morally wrong, probably not, but slightly imprudent, perhaps?). Now something like substance abuse to deliberately frustrate one's rational thinking and overly heighten emotional gratification would be an egregious frustration of rational animality.
I think currently the typical lay person has an interesting blend of both of these classical natural law interpretations. We tend to classify what's bad or wrong for a natural substance by judging it against its universalized nature. We call someone handicapped or mentally ill insofar as they don't instantiate what is thought of as a healthy human being. But we also emphasize dealing with one's lot in life, coming to realistically understand one's limits, one's talents, etc. And no doubt there are many Christian circles that view God as a giant Fate modulator, seeing tsunamis, fires, terrorist attacks as divine providence, and that we ought to come to peace and security in God's will for the cosmos.