The problem manifested when the .py module got reloaded and the corresponding extension module didn't. The .py module registers types with the extension and the extension was not allowing that to happen more than once. The solution: let it happen more than once.
This brings the code under test.support.interpreters, and the corresponding extension modules, in line with recent updates to PEP 734.
(Note: PEP 734 has not been accepted at this time. However, we are using an internal copy of the implementation in the test suite to exercise the existing subinterpreters feature.)