Very interesting situation you describe.
I think a solution would be to lobby the airlines to allow passengers to enter two documents: a travel document to exit the origin country (used for the departure APIS) and another one to enter the destination country (used for arrival APIS). Apparently, the technology exists, but they have not been willing to implement it.
I can't believe this isn't an option yet, given the amount of people that have dual passports. It shouldn't be that hard to implement really.