After discussing with Andrea Boriero, I've decided on a simpler approach.

hibernate.native_exception_handling_51_compliance will be added with possible values true or false (default). This property will indicate if exception handling for a SessionFactory built via Hibernate's native bootstrapping should behave the same as native exception handling in Hibernate ORM 5.1,

When set to true, HibernateException will not be wrapped or converted according to the JPA specification.

This setting will be ignored for a SessionFactory built via JPA bootstrapping.

I've updated the description above to reflect this change.