There you go, contradicting yourself.
First you claim you can NOT change the sex of an embryo, but then admit you can by saying it is "very hard".
Of course it is hard.
No one said it was easy.
But you don't do it with a pin.
You do it by massive hormone imbalance.
And the point is it DOES happen.
It happens from illnesses, pesticides, DNA malfunctions, etc.
And the % of people it happens to is rapidly increasing, as we contaminate food, water, etc., with pesticides and herbicies, (which are basically strong hormones).
Here look, I'll give you one for free. You are smart, and interested, so you deserve it. I can "not" share what I know in a short post, it would take years. And, I don't want to get into the credentials game, but since I already mentioned it in another thread, I was a working experimental gender biologist for a while, in the laboratory of Simon LeVay (Google is your friend) just after he arrived at the Salk Institute. I'm not published in that particular field, but "I know a little". Kay?
So here's what I'm going to give you for free, and if you work with pacemakers you definitely have enough education to understand this.
Human development (including embryology) is all about chemical gradients. Even the single fertilized cell, already knows which end is the head and which end is the tail. When the cells divide, they communicate, to maintain the required gradients throughout the organism.
The reason the pin experiment works in the tadpole, is that when you stick the pin in, you're disrupting a chemical gradient. You can't just stick it in willy nilly though, it has to be very precisely timed and at exactly the right place, which is not an easy thing for a student to learn. However this is just ONE gradient we're talking about, depending on the timing it might be something like a COX-6 that determines body segmentation.
But in sexual development, as you probably already know, there are DOZENS of interacting gradients, in different places at different times. If you just stick a pin in, the results are completely unpredictable. Yes, you can get sophisticated. Or try, anyway. But it's hard, it really is.
What you're basically talking about in such a case is a complete reprogramming of the organism, you have to effectively "play God" and make all the chemistry conform to your new plan instead of the existing gene expression.
Okay, so, you said something about anomalies being in the 1% range, and that's approximately true, but that's "aggregate" anomalies, so like, male female and other. Politically, I would prefer we treat everyone as an individual, and anyway, the law is SUPPOSED TO be blind to race and gender and things like that.
Funny story - for a while I worked at a large medical provider, and during the Y2K thing they said well, as long as we're doing that we're going to do genders too. Only, they didn't add a field, instead they tried to cram it all into the existing field. So they ended up with - count em - 67 gender varieties. (Male straight, male gay, female straight, female gay... that's the way they did it. I guess the software people didn't talk to the doctors. lol)

They only got rescued from this mess when they spent 4 billion dollars on a new enterprise computer system.