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Michael, can you checking some of this in as separate pieces?

The __module__ relaxation should go in first, and marked as
backport candidate.

The __name__ fix is close, but I think it *should* be
allowed to put dots in the name (this is actually a feature
for old classes); instead of '.' I want a check that there
are no \0 bytes in the string (see set_name() in classobject.c).

I think the restrictions on __bases__ are sufficiently
thought out; with old-style classes, you can do much more
class switching:

>>> class C: pass
>>> class D: pass
>>> D.__bases__ = (C,)
>>> 

I'd like this to work for new-style classes too. It means
that __base__ has to change though.

There's a bug in set_mro(): it checks PyInstance_Check()
where it clearly means PyClass_Check(). Other than that I
think it's good to go. (Though this is the ultimate weird
feature! What's the use case again?)

Hoping for unit tests,