I think perhaps we should admit that this build system is no longer supported. From everything I can tell, the mingw project is no longer maintained. The project's site, mingw.org, is no longer live; the project on sourceforge, although still downloaded daily, had its last commit almost 3 years ago - a commit which changed the official project URI to a new link that now is also dead.
Looking over BPO there are a little over 50 bugs open against mingw, but only 7 that have any meaningful activity within the last three years. Three of those issues explicitly mention mingw-w64 which is an active fork of the original mingw project (active homepage, commits almost daily, new release within the last 6 months) and I wonder if this is the project the other 4 projects meant by "mingw"?
Ideally any features and flags in the code base for mingw would be checked to already be working with mingw-w64 or else modified to work, but this would require a sponsor for this platform, which appears to be missing. Further, there is no buildbot for mingw, which should be a requirement to be a fully supported platform, as per this PEP. This potential work appears non-trivial with a cursory look at the mingw-w64-python pacman project, which contains close to 100 patch files. I am purposing instead that mingw be deprecated and, if a sponsor comes along, mingw-w64 can become re-supported, or newly supported depending on you point of view, as allowed by the PEP.
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