So, you can throw in the towel or get out the heat gun. In a couple hours you can remove all the old glass, get rid of those white specks and sand back to bare wood.

Ask anyone here, who has fixed mistakes, how much time they wasted thinking about the mistake and how fast and easy it was to fix it. It's called experience.

Rob

And I don't think any amount of transparent dye finish will hide white flecks in the glass, as they (IME) tend to 'catch the light'.
I've sprayed a few sunburst guitars and it was surprising how 'dark' the lacquer had to look in the mixing jar, to look right when in a thin layer.
I wouldn't add any pigment to a clear finish - might as well stir in some mud, IMO. But I never did like stains with pigment even on bare wood - dyes are a whole lot better-looking. I've used the ColorFX dyes and they perform well. In Canada, WoodEssence sells them.