I can use a set of AWS API commands to associate a VPC with a private zone hosted in another account. That way, name resolution works in the VPC even for the zones that are defined elsewhere.
Here's the relevant documentation: https://aws.amazon.com/premiumsupport/knowledge-center/private-hosted-zone-different-account/
However, I have no idea how I can see what zones a given VPC is associated with. Does anyone know?