Get rid of DIRECTORY_SEPARATOR

This is a first tentative of standardizing on `/` as the directory separator (in Windows too...) and render the usage of DIRECTORY_SEPARATOR unneeded.

It **seems** to work but thorough testing is needed, especially under Windows.

I'm unsure of what I did with unit tests: they should be particularly screened and tested
I think this assumes that the paths being fed into this method will always use a `/` separator.  This would be one of those places where the paths should be specifically modified to standardize on the `/` separator.  As it's a public API method, there's no guarantee that callers will have done that before calling this method, which means this change might cause issues with a `C:\Windows\system32\` style file path with the trailing slash.