The point is that Ian Stevenson's work is not speculative. It is scrupulously empirical. There are instances such as those you refer to in his cases - birthmarks that replicate injuries. Stevenson does not elaborate or speculate much - in fact his writing is very dry. That is why the Shroder book is useful although once you get over the 'gee whiz' factor it is not so remarkable. And it is one of the only sources of actual information - as distinct from speculation, folklore or myth - that you will find on this question. So can't really see why you are so keen to brush it aside.
Buddhist doctrine about rebirth is paradoxical. The Buddhist idea of annatta is usually interpreted as meaning that there is no soul or abiding identity. However it is impossible to reconcile this understanding with such practises as the selection of successors of the Tibetan Rinpoches. The whereabouts of the new incarnation will be divined by a dream or an oracle, and then he will be shown items belonging to the previous incarnation, and so on. How you can reconcile this with the idea of 'no soul' is frankly beyond me. Buddhists employ a lot of sophistry to maintain this position, in my view.
Buddhism discourages metaphysical speculation and clinging to ideas about soul, self, or anything of the kind. But there are grounds for saying that the Anatta doctrine does not mean 'no-soul'. It means that everything is without self
. Ear, eye, nose, taste, etc, these are not-self. Every phenomenon is without-self or not-self. This, however, does not mean there is no soul.
What do the Nikayas have to say of the Self? "That's not my Self" (na me so atta); this, and the term "non Self-ishness" (anatta) predicated of the world and all "things" (sabbe dhamma anatta; Identical with the Brahmanical "of those who are mortal, there is no Self", (anatma hi martyah, [SB., II. 2. 2. 3]). [KN J-1441] "The Self is the refuge that I have gone unto". For anatta is not said of the Self but what it is not. There is never a 'doctrine of no-Self', but a doctrine of what the Self is not (form is anatta, feelings are anatta, etc.).
Contextual doctrinal examples being: "The Self (Attan) is Charioteer"[J-2-1341]. "Ananda, dwell with the Self (attan) as your Light, with the Self as your refuge, with none other as refuge." [SN 5.154, DN 2.100, SN 3.42, DN 3.58, SN 5.163]. "The Self (Attan) is ones True-Nature (Svabhava)" [Mahavagga-Att. 3.270] "The Self is the refuge that I have gone unto; it is the Light, that very same sanctuary, that final end goal and destiny. It is immeasurable, matchless, that which I really am, that very treasure; it is like unto the breath-of-life, this Animator."[KN J-1441 Akkhakandam][Source
Furthermore, the way Buddhism developed under the Mahayana adds such notions as the Buddha-Nature and the Trikaya (triple-body of the buddha), and the idea that the Bodhisattva will willingly re-incarnate for the sake of all beings.
So be careful in what you attribute to Buddhist doctrine of no-self and re-birth. It is a very deep study.
Other references: The Buddhist Unconscious
by William S. Waldron
The Dance of 17 Lives: the Incredible true story of Tibet's 17th Karmapa
, by Mick Brown.
Let me observe that your approach seems very impatient.
All the best with it.