There's a key difference with the glasses analogy, though.

In the case of glasses, we know that there are eyes. We know the whole causal chain, at least in outline, from photons being emitted through to visual cortex detecting features. We know explicitly what role glasses play.

The problem with using this as an analogy is that we have the causal chain for neuroscience too! We know how neurons work. You can't just invent a spirit of the phlogiston that makes engines turn--the gasoline and combustion and everything merely unlocks the engine's experience of the spirit of the phlogiston--because all the pieces are adequately accounted for.

And thus it is with neuroscience. The pieces aren't all in place, so it's true that there's a little room for some odd physically supervening force...but very little. And if there is no physical supervening force, then consciousness is causally completely impotent, which certainly doesn't comport with our experience of it. Again, we don't have the neuroscience perfectly worked out, but studies of the effect of attention are pointing exactly the way that we'd expect if consciousness in fact is causally potent.

So analogies aside--and a few odd observations aside (leaving out the many, many non-odd observations, and also with the odd ones' oddness overstated--for instane, even though our bicameral minds do a lot of redundant computation, you can absolutely tell that there's something wrong: https://www.caltech.edu/about/news/patients-missing-one-brain-hemisphere-show-surprisingly-intact-neural-connections)--there is really a spectacular amount of not-quite-airtight but more-than-we-demand-for-most-other-things evidence that the mind is computed by the brain and it's all a physical process.

That it offends our intuitions that our minds could be computed is more a statement about poor self-introspection than a fundamental flaw in our research.

Regarding the evidence for reincarnation, I don't have the time to conduct an extensive review myself, but the shape of the evidence is very troubling. You have multiple phenomena with key compelling features that express in only small subsets of the data. For instance, the tiny fraction of cases with no contact (~1%) is highly consistent with a model where the information is in fact being relayed to the child through conventional means. That you lose track of how information got conveyed one time in a hundred would not be terribly surprising. The anecdotes are not properly controlled: what is the frequency, for instance, of young children reacting negatively to someone who has committed some horrible crime? There are plenty of anecdotes of dogs picking up on something not quite right about people--why not children?

Selection can confound one's intuitions about rareness fantastically. Suppose, for instance, that I roll 100 dice, and 16 of them come up as 6. Now, I pick out these 6s, and ask: were these really random, or was the God of Luck making them happen? Let's see. (1/6)^16 = 3*10^-13, which is fantastically improbable! Clearly, this is no random event: it was the God of Luck for sure!

What went wrong??

So, if you don't have a good handle on the probability distribution of coincidences, and the phenomenon overwhelmingly seems to admit the possibility for side-information of the type that we know full well can happen, and any possible mechanism is strongly at odds with a great deal of research, the appropriate stance is to be highly skeptical. Even the birthmark/physical deformity has a path for going the exact opposite way: person sees child, person knows about other event, person talks about event (maybe to child, maybe not), child picks it up.

People really underestimate what children pay attention to, too. Just this morning my wife and I were discussing plans by ourselves; we mention, amid other things, that maybe we should look into rock climbing. Instantly, from the next room over, despite being busily involved in something else and having displayed no sign that she had heard anything else we said (and us talking quietly enough that we wouldn't have thought she could hear us), our daughter immediately pipes up, "I want to go rock climbing!"

In the face of things like that, we need to be profoundly skeptical of claims that the children had "no way to know" something.

So, on the one hand we have a very pedestrian explanation consisting of things we know quite well: children are imaginative, children are perceptive, intuition is poor regarding probabilities of coincidences, information can flow the opposite way you expect.

On the other hand, we have a radical rethinking of the nature of the physical world.

Hmm.