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I'm not sure that it could work because many C functions use caches using static variables.
Just a random example:
int
_PyUnicode_HasNULChars(PyObject* s)
{
 static PyObject *nul = NULL;
 if (nul == NULL)
 nul = PyUnicode_FromStringAndSize("0円", 1);
 if (nul == NULL)
 return -1;
 return PyUnicode_Contains(s, nul);
}
If hash(nul) is computed in an interpreter, the same hash value will be used by all interpreters. If interpreters use a different hash secret, you will have a problem.