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Thank you for your analysis.
I'm not intimitely familiar with the bytecodes, but one way
would be to omit the writeback (STORE_SUBSCR) if the result
of INPLACE_OR is identical to its input. This could probably
be done without changing the bytecodes but might profit from
some changes for speed and compactness.

That is (pseudocode):
_t1 = t[i]
_t2 = inplace_or(_t1, a)
if _t2 is not _t1:
    t[i] = _t2

Another variant would be to add indexed variants of the
augmented assigment methods; that is, augmented variants of
__setitem__, but that has other drawbacks. However, it might
be useful in its own regard in some cases.