I agree to what you write here, though I haven’t watched the video, and of the names you mention, I’m only familiar with Jaki who I admire philosophically as well as scientifically.
However, it’s important to remember that Jaki’s criticism against the phenomenon we call scientism (which is what I think you mean by empiricism, or am I wrong?) also hits “theologism” (if that’s a word). The main fallacy of the scientism crowd is that they think natural sciences, which are only concerned with the material, can tell us something about the metaphysical. At the same time, the “theologism” crowd think theology, which is mainly concerned with the metaphysical, can tell us something about the material world. Both of those ideas constitute category mistakes.
Which is why I cringe just as much when I see the Christian (mainly Protestant) trying to use the Bible as a science textbook, as I do when I see the Atheist trying to use natural sciences to disprove God. Both fallacies are manifestations of ideology, defined as letting a particular science become the all-explaining/“omnipotent” science. Philosophy, however, transcends science, and can hence say something about other sciences, but philosophers should know their boundaries too - they tend to embarrass themselves when attempting to use quantum physics for philosophical purpose, for example. Note that I know less than I wish I did about quantum physics, but I have this from a physicist
I’m not sure if I’m one of the skeptics you were referring to, but either way, I certainly am a skeptic, toward science (at least!) as much as everything else. I’ve spent too much time with “brains in a vat”-style arguments to think of empirical science as definitive in any way. If I weren’t Catholic, I wouldn’t even believe in the existence of an external world. But when discussing science, I (do my best to) do so within the boundaries of science, since its domain doesn’t converge with theology, and not really with philosophy either. The
ethics surrounding science surely does, but ethics of science isn’t science, it’s something that governs science. The same goes for methods of science - the current scientific method came into existence because of philosophy, and philosophy may very well (or probably will) be the discipline to change that at some point in the future.
Interestingly, my views make some Atheists (and even some Catholics) see me as a horribly conservative, superstitious and irrational person, while some religious see me as a horribly liberal, secularized closet atheist. Which is both entertaining and frustrating, but then I guess pleasing no one (or well… “few”, I guess - I know some like minded people) is better than pleasing everyone…