Another way to save the post-processing approach that would probably be easier than testing for something already up there would be to lower the top coordinate of the polygon of the white background by subtracting font-size. That would give you some new space on top for the text that should be free of anything else.
(Probably need slightly more than font-size, in case parts of some characters descend below the baseline).
(Probably need slightly more than font-size, in case parts of some characters descend below the baseline).