I think it's time to test wiring as replacing both switches with new should have cured the problem.
The original way it was wired should have worked correctly and it did for many years, I've even wasted my time and double checked by mocking it up.
Wired this way the intermediate will do nothing and the light will be on in both positions of the 2 way switch, maybe a quick flicker when switched over.
This is only a test of wiring and the 2 way switch, I'm not suggesting it as a wiring solution.
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