You can always fit an experience on that Gaussian curve. The peak of the bell would be “egg breaks” and the respective extremes could be “egg floats”, “egg disappears into the ground”, “oh, the egg is not an egg”, or something analogous. But that's just a minor thing. Though pretty telling in light of quantum mechanics – when you throw gazillion of coins (i.e. “particle-waves”) you get normal distribution which is just a special case of binomial distribution with sufficiently large number of tries.

Anyway. Science does not exclude the anomalous. Quite to the contrary – science gets more and more refined because it encounters the anomalous and must update its explanations to account for it (if it wishes to remain valid science). That's its very nature. Heck, a lot of discoveries was made because the experiments that were searching for something revealed something else entirely due to wildly unexpected (i.e. anomalous) results.

I would say that you have a problem with scientists who became priests of academism and project your disagreement on the science itself. Even so, there is a huge difference even between Dennett, Harris, or Dawkins, let alone between them and the likes of Chalmers, Kastrup, or Goff (even though the latter are philosophers).

Furthermore, our lives pretty much depend on explanations. So, “the compulsion to fit reality into a rational model” is rather pragmatic, not a “fool's errand.” While reality does not care about our models, indeed, their accuracy has existential implications for us. If you cannot fit approximation of reality into a rational, testable model, your model is simply divorced from reality with disastrous consequences. Well, majority of human population believes in immaterial souls, spirits, etc. and it definitely reflects in the state of our societies.

All in all, science, despite its many limitations, is hands down the best model we have. It's only natural (and desired!) that in 3023 our current iteration of it will “look like superstition by then.” (Though, works of e.g. Pythagoras, Newton, etc. can be hardly considered superstitions even today.)

Regarding the experience of soul – as I asked in the OP, what exactly is that experience and how do you trigger it? (I can sort of imagine why people came to the faulty assumption that they have soul, but still.)

As for how any of that anomalous and extraordinary fits “into a physicalist, deterministic model of reality”, I've already written about it extensively.

https://senderspike.medium.com/heaven-on-earth-7d83596d4a0b

https://senderspike.medium.com/mind-brain-and-consciousness-9127f14dea4

https://senderspike.medium.com/no-one-here-gets-out-alive-f7a2a1db75

https://senderspike.medium.com/what-color-is-red-2c7cf7cb40db

https://senderspike.medium.com/mystical-perception-2e8ce7457c99

https://senderspike.medium.com/absolute-equivalence-b4584dc2e290

https://senderspike.medium.com/quantum-observer-466e61f8d4b9

https://senderspike.medium.com/tree-of-life-2d7b5f28eda2

https://senderspike.medium.com/god-is-a-materialist-d84fd80e3f30

Etc.