There are no 'reasonable possibilities' by which one person could remember things that happened to another. There's not really anywhere to go from there.
It seems that what you want to do is to divorce our understanding of reality from actual events, and to proceed from theory to understanding without testing theory against reality. It's a fruitless and sterile approach, because there's no method by which it can be corrected should it fail to agree with reality. The scientific method is a superior approach; formulate a theory, determine what would be required to falsify that theory, test it against specific cases (this is the bit where reality impinges), and accept or reject it based on whether it has yet been falsified. If you remove the bit where theories are tested against specific cases, then you're discussing fantasies rather than reality.
So unless you can come up with a case that specifically refutes cryptomnesia, then you don't really have an argument, because cryptomnesia doesn't violate the theoretical structure that has been extensively tested against actual cases, whereas actual remembrance of past lives does; cryptomnesia is therefore a more parsimonious choice.
Dave
Here's a case I think makes cryptomnesia an unlikely explanation, at least for this case: https://www.youtube.com/watch?v=SZbyaGvlzPE