Hardly in sense 1d is used sometimes with not for emphasis.
In sense 1e with a negative verb (such as can't, wouldn't, didn't) it does not make a double negative but softens the negative. In "you can't hardly find a red one," the sense is that you can find a red one, but only with difficulty; in "you can't find a red one," the sense is that red ones are simply not available. Use of hardly with a negative verb is a speech form; it is most commonly heard in Southern and Midland speech areas. In other speech areas and in all discursive prose, hardly is normally used with a positive.