Hi Daniel-
The problem is probably not with the mic or mount, but with the clothing itself; if it’s a silk, satin, or nylon type material, it will cause noise that you might not otherwise hear with your ear but, the mic picks it up (like a tie or even a suit jacket). If the shirt has any starch in it, that can cause noise, too.
I had a nightmare shoot one time where a woman had on a period dress made out of satin; no matter what I tried, including making a baseball size wad of tape and putting the mike inside it, all a heard, was clothing noise.
If you think it’s the cord, try taping it (the cord) on the inside of the jacket using 2 inches of 1″ camera tape (near the clip).