Not sure how much this would help, but here's something I've come across.

http://www.newliturgicalmovement.org/2016/08/miracles-new-film-from-st-anthony.html#.V6nmKjS3K_8

There are scientists and philosophers of the last century or so, including today, who would argue that the evidence for various paranormal phenomena is fairly well established. In the work Irreducible Mind[i]​,[/i] edited by Edward and Emily Kelly, the contributors, who are all psychologists or philosophers I believe, make just that claim about psi phenomena and various other paranormal phenomena such as NDEs and OBEs. They also note there are well established mental phenomena that can't definitively be called paranormal but that seem very hard to explain on a materialist viewpoint (well, technically, as the authors note, even many normal brain functions, like memory and intentionality, pose problems for materialist understandings, but we can leave that aside) such as extreme psychophysical influence, hypnotism, aspects of autonomism, and aspects of memory and genius.  

​The philosopher C. D. Broad fifty years noted that those who dismiss paranormal phenomena out of hand tend to be ignorant of any real understanding of the topic.
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​So, I would say that much of the lack of acceptance is due to a combination of materialist assumptions and ignorance (most scientists know little about the experiments and evidence on these topics) There is also a lot of misinformation and dubious practice and methodology amongst sceptics, or pseudo-sceptics, that arises from ignorance and an inability to look past materialist assumptions and compounds these problems. For example, it is quite shocking how often supposedly sceptical investigators will misrepresent accounts and findings. There is also a pattern of trying to come up with just about any other explanation, even one that doesn't fit the facts, and then acting as if the whole incident is debunked. This attempted refutation will then get passed down to other sceptics, and the thing treated as settled. It must not be overlooked how strong devotion to materialism is in some scientific quarters, such as neuroscience and much mainstream psychology. Even a hint of dualism is considered a betrayal of science.

​The methodological problems of the sceptical position include the unwarranted dismissal of spontaneous cases. This means that the sceptic simply refuses to accept any non-laboratory cases, no matter how well documented. They also include the designing of obviously flawed studies - most glaringly the so called undergraduate model, where random undergraduates are used to test phenomena that take knowledge, time, and interest or aptitude to develop. An example, is tests into extreme psychophysical influence under hypnotism. Such influence has certainly been shown and well-documented, but it usually only takes places amongst those particularly susceptible to hypnotism - or sufferers of hysteria. At the very least it takes quite some time for someone to become hypnotisable enough for any chance of it occurring. But one researcher, a sceptic, decided that it would be good to test this phenomena by enlisting student nurses from a local hospital and, with little prepping, try to hypnotise them and exert such psychophysical influence (here the manufacture of blisters simply through suggestion). The classic example is trying to study the possible effects of meditation by studying undergrads with neither knowledge nor special interest in the techniques.

​I don't doubt there are conscientious sceptics, but I'd suggest being as sceptical of sceptics as you are of those making paranormal claims. The work of members of Society for Psychical Research - such as Myers, Gurney, Sidgwick, William James, and others - must rank as some of the most scrupulous scientist work ever done in any field, despite predictable chirping from pseudo-sceptics.

​I would strongly recommend reading Irreducible Mind​, both for its introduction into extreme mental phenomena - some clearly paranormal, some potentially so - and its appendix that lists many good works on paranormal phenomena. Stephen Braude is a contemporary philosopher who takes these phenomena seriously and has written on the relationship between them, science, and philosophy.

Well, yes, dismissals mean nothing if they aren't well-informed and well considered, and most aren't, even amongst so called sceptics. Some of the attacks on Stevenson are the usual kind you find amongst sceptics - almost anything they can think of. One is that he sometimes relied on interpreters. He knew several languages but of course not all. So he sometimes relied on interpreters. But this in itself is hardly a problem. He took pains to get reliable ones, and it isn't obvious why an interpreter must be a problem.

Stevenson is good on research, but he is less good on the meaning of his research. He makes a cogent case for ruling out non-paranormal explanations but is less considered in addressing the underdetermination of the evidence as concerns paranormal explanations. Or, in other words, he is better at ruling out mundane explanations than showing reincarnation must be the best explanation.

In these empirical investigations I wouldn't take Stevenson on his own. The work of Gurney, Myers, Rhine, and the rest should be added to Stevenson's. But as evidence for the paranormal, and certainly as problematic for materialism (leaving aside reincarnation itself) Stevenson provides very suggestive evidence.

By the way, he wasn't just an investigator of reincarnation. He did interesting work into other areas of psychical research, such as into mediums (he investigated the interesting case of Runki's leg, for example).

In the end, though, if you are interested in these topics, you have to look into in some depth yourself. From the outside it is hard to know whom to trust. You certainly can't trust everyone claiming to be a sceptic, even those claiming to have researched the topic. A lot are pseudo-sceptics, dogmatic materialists the mirror of the most credulous new agers. But, of course, neither can you necessarily trust even every informed believer.

Apart from the Kelly's book, ​Irreducible Mind​ (which, as well as genuinely paranormal phenomena, contains interesting sections on unusual phenomena that even if they aren't paranormal per se, are at least very hard for materialist explanations of mind to explain, like extreme psychophysical influence; some hypnotic phenomena; some aspects of autonomism, genius, and memory), I recommend Stephen Braude as good introduction to some of the issues of psychical research - both on the research itself and its philosophical meaning. Gurney et al's Phantoms of the Living and Myers Human Personality are also very worthwhile early works to look into. The Parapsychology Revolution is a recent compendium of writings on psychical research from the days of Gurney, Myers, and William James to today. From a more cultural anthropological/history of religion perspective, Jeffrey Kripal's ​Authors of the Impossible is worth a read.

I think that the case for reincarnation per se is not supported by Stevenson's evidence. I think it unlikely that mundane explanations - fraud, cryptomnesia, and so on - can explain them. Stevenson, despite the usual insinuations from pseudo-sceptics, was a thorough and honest investigator. I think he pretty successfully rules out the obvious, natural explanations. But there can be numerous non-mundane explanations, of which it is hard to chose, absent one's metaphysical assumptions. Not only is there the perennial controversy within psychical research of survival versus what is called super-psi (or psi-phenomena amongst the living), but explanations such as demons (although the demons hypothesis seems to me to suffer from the somewhat tedious Christian need to categorise all psychic or subtle entities - part of which includes what C. S. Lewis called the Longaevi and Tolkien Faerie ​- into either demonic or angelic beings)  and the transference of psychic elements short of the whole soul or self are hard to rule out.

I'm not sure how reincarnation fits into Platonic or Aristotelian metaphysics, although Dr. Feser certainly thinks that it is contrary to hylomorphism (although some neo-scholastics did not, I believe). Someone on one of Dr. Feser's threads on this topic posted this interesting link:

http://www.studiesincomparativereligion.com/public/articles/Reincarnation-New_Flesh_on_Old_Bones-by_Whitall_N_Perry.aspx

​As Perry implies, even within Hinduism (and certainly Buddhism), it is far from certain that the popular interpretations of reincarnation (as in the central self in some sense reemerges in different physical bodies - whether that self always has part of its existence outside any particular body or not) is the interpretation of philosophical Hinduism. He also notes something sometimes missed in assessing Stevenon's findings - the often neurotic (or worse) nature of the subjects. If Perry is correct (and he may be exaggerating and cherry-picking somewhat), this does add an interesting dimension to the issue - it doesn't seem a mark of psychic and spiritual health to suffer these phenomena.