Study the details in the compelling cases. Delusion can not explain knowledge of verifiable details. And these cases follow very similar patterns where researchers painstakingly look for normal explanations.
The evidence for reincarnational memories is through thorough study of anecdotal evidence considering all evidence and argumentation from all possible sides and all possible theories as to what is going on.
Allot of theorists are now suggesting that memory is non-local. And consciousness itself is non-local. The physical brain is then an organ that allows consciousness to experience the physical realm.
The subtle bodies, soul, astral, mental have senses that allow them to experience their native plane/realm just like our five senses give us information about the physical plane. Advanced and gifted people have abilities to use these subtle senses while in the physical body to see more than we do.
I think the physical-only model will never give us a full understanding of consciousness, subjective experience and paranormal events. These subtle bodies interpenetrate the physical body and information moves between the bodies through sympathetic vibrations above the physical plane. If you study esoteric literature on these subject you can see explanations of how this all works in detail. But, predicting your question
, 'no' this can not be verified through physical senses and instruments.
After years of study I have come to the belief that the eastern/Vedic/Hindu model of the universe explains things more satisfactorily than the physical-only model.