Would this be decent evidence for reincarnation?

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Statistically they are meaningless without evidence to back them up.

This is the evidence in question. The past life memories of young children. This is something you can put to the test but unlike most paranormal claims we're looking at a statistically significant hit rate with an absence of any of the usual con-artist techniques. Sure it's not proof of reincarnation as there may potentially be another explanation for it.

They very well could be evidence of something, which is to say, they could be evidence of nothing at all.

There will have to be a good explanation for this high level of accurate predictive statements. If someone can get 9/10 details right there is a reason to explain how they are able to do this. Reincarnation is suitable explanation, certainly the children themselves claim to have lived before. No reason we know about why they couldn't have done, yes so we don't know how it's supposed to work but I'm sure we don't know quite a lot.

But, again, that does not thus equate to the thesis of reincarnation being right. You're putting the cart before the horse and presuming the thesis is correct using the suppositional 'evidence' that is provided. This is the wrong way around.

It would be a straightforward explanation for how a child can know details of a former life. You don't have to go out of your way to make it more complicated if you don't have to. No reason we know of why that couldn't happen it's well outside of our knowledge or experience of the world. Whether it means religions had it right it could just be a lucky guess on a certain detail.

Eliminate all other possiblities. What you are left with must be a semblance of the truth.

If an explanation is straightforward and would fit the evidence you have then there is a high probability that it is true.

The research currently conducted seems eons away from that at the moment.

It's probably because 95% of scientists share your attitude to anything like this and won't want to touch it with a barge pole. This isn't getting properly researched. Same goes for a number of other phenomenon that are poo pooed.

It could be explained away perfectly by natural, easily verified data.

By chance you're only going to get a certain hit rate of guesses. If you have something significantly better than chance then something significant will account for it.

It could be nothing, just a blip of coincidence.

If it was just one case perhaps but it occurs throughout the world and in all cultures including cultures that don't generally believe in reincarnation such as our own.

It could be lies.

Young children aren't very good at lying, you can tell because they cover their mouths with hands as though to conceal the lie. Adults are much less obvious and may touch their finger to their lips briefly.

Not good enough. 'Apparently the best explaination' to me = no evidence, just presumption and guesswork. Again, I refuse to accept this as 'true' until all avenues of exploration have been conducted and all other explanations dismissed. This is not the case. Even the book you cite admits this.

We have evidence of something interesting and now we have to find a good explanation for the evidence we have. A good explanation is that consciousness is somehow separable from the body and can be transferred into other bodies via some kind of process we don't as of yet understand. There could potentially be a better explanation if you can think of one.

Parsimony doesn't equate to adequate, especially not in this case, and especially when the data is so lacking.

I think the data is lacking because it isn't being seriously researched. To many scientists something like this would be the equivalent of a religious heresy as they're deeply invested in a materialist worldview this wouldn't really support.