Fish are able to change sex to adjust an imbalance in the sexes. It seems that humans are going for the same ability.

Well, a lot of fish are able to change their sexes after birth. I believe with humans, its stress hormones effecting the fetus and biasing the gender. At least from an evolutionary standpoint, stress means conflict, conflict means males dying, replace them or the species dies out. Things that take millions of years can't keep up with boom sticks that fire projectiles.
Since this is the case (I presume), all it means is that if the kids hadn't been vaccinated in November-December, there would have been such a dynamic drop in SIDS that we could for certain blame the vaccines for the SIDS deaths.

I'm not sure that I'm following 100%, but what you are looking to see is if changes in routine vaccination schedule due to covid results in any difference in pregnancy outcomes. To this point, there has been no routine vaccination schedule change for any babies that have already been delivered. I did a quick google search because my only background was that when I get a flu shot, they ask me if I'm pregnant, to which I always respond yes, and it pisses them off. Anyway, between that, and a quick CDC guideline that said make sure your MMR shots are up to date before becoming pregnant, leads me to believe that they don't normally give you vaccines while pregnant. If we're just talking about the US, routine vaccinations were still in place in March anyway, maybe April or later in some places. What that means is that anyone who got pregnant before April (more realistically May) received all of the regular vaccinations that they would have normally, so any babies delivered until 9 months after that date is just a regular ole vaccine exposed baby like the rest of us.
While I doubt that we'll see the outcomes you're expecting, I'm with you in being interested in how covid effects birth rates, etc. Will many of the children born be male, will there be a new baby boom generation because couples have been stuck home with nothing better to do, will being exposed to covid or the covid vaccine result in tails and horns, lets watch!