I am very, very nervous about doing this. This is not how native ddraw behaves on windows 98 (I checked), and we have other bugs that are caused by us messing with window styles.
The fact that newer Windows versions behave like this isn't really an argument. Newer Windows tends to break a lot of ddraw games in various ways.
I think the ideal way to fix this, and the aforementioned other bugs, would be to manually escape into the user driver rather than relying on GL or Vulkan WSI. Possibly this would use D3DKMTPresent(), although I'm not entirely sure how. I believe Henri (@hverbeet) has an idea of how to achieve this?