Font Renders Poorly in Web Browser, Good Everywhere Else

It is one of the Frequently Asked Questions

By copying the glyphs to a new font, you lost the hinting.

Instead, save the original font three times with three names, and delete the glyphs that you don’t need from each.

If you need to add the mappings to the Alternate glyphs so that your users can access them, copy the glyphs with the desired mappings before you delete them, and use “Paste Special” to paste the mappings to the alternate glyphs (which probably don’t have any mappings),without copying the glyph outlines or metrics, overwriting the existing mappings.