Given the lack of response to my clarifying questions over a week later, I'll supply a deconstruction anyway:
Your argument seems to be something like this:
1. There are no causes of natural phenomena other than natural causes.
2. Subjective experience is not a natural phenomenon (implicit).
3. Subjective experience is causally inert.
4. Subjectively experiencing beings (such as us) have knowledge of our subjective experiences.
5. Our knowledge of our subjective experiences cannot be explained by natural phenomena nor by subjective experience itself (given #1, #2, and #3).
6. Therefore, our knowledge of our subjective experience is supernatural ("designed").
A lesser (semantic/terminological) problem with this argument is that it conflates "natural" with "physical", and "supernatural" with "non-physical" (in my first post, I alluded to this conflation without calling it out as problematic). This is problematic in particular because most people would agree that subjective experience is non-physical, but not that it is supernatural. I'll otherwise simply run with that conflation in what follows.
The main problem with this argument though is that it simply assumes the truth of premises #1 and #3, without justification. In my view, both are false.
To see why, let's assume that they are true and that the conclusion is sound. We can then show by a sort of reductio ad absurdum that the scenario in which at least one of them is false is rationally more appealing than the scenario in which the conclusion is true, given how rationally unappealing that conclusion is:
When subjective experience is entirely epiphenomenal (caused by natural processes of the brain)
except for our knowledge
of those subjective experiences, which is supplied to us supernaturally, then we have a sort of special pleading, which is thus rationally unappealing, but, additionally, this scenario suggests another rationally unappealing conclusion, especially given the theistic (protestant Christian) motivations underlying the argument: a denial of free will. If experience is entirely caused by (1) natural phenomena, and (2) divine intervention, then there is no room for personal agency.
If, instead, we allow that premise #3 is false in at least the limited sense according to which subjective experience is causally efficacious
with respect to itself, then we have no need for special pleading to explain premise #4: in this case, we have knowledge of our subjective experiences simply because those experiences
themselves cause that knowledge in us (i.e., in our own, self-reflexive, experience). Moreover, we don't have to deny free will if we additionally posit that our experiences occur in the context of a non-physical mind (aka soul) which in a holistic sense has personal agency, i.e., it is not wholly determined by natural phenomena like the brain plus special-case divine intervention.
If we then extend that falsity to allow that subjective experience (in the context of each of our non-physical minds) is causally-efficacious with respect to physical phenomena too (including the brain and its processes), and thereby falsify premise #1 too, then we can explain how the intuitive reality that our experiences, such as pain, have real physical effects is correct. We don't, then, have to deny this intuitive reality as you do in the video.
I think it's pretty clear, then, that denying premises #1 and #3 is more rationally appealing than accepting your argument's conclusion.
Related arguments in other Psience Quest threads:
Analytical argument against physicalism. This argument works with similar intuitions and premises as yours to falsify physicalism (which you seem to equate with naturalism).
The Mystery of Psycho-Physical Harmony. This is an argument for theism that might excite you. It works in similar territory: the (strangely harmonious) relationship between physical phenomena like the brain and body, and subjective experience.
Generally, the alternative scenario I suggest (in which premises #1 and #3 are false) is almost certainly more compatible with theism than with atheism, so you need not reject it on the basis that it flies in the face of your religious beliefs.