I haven't sewed anything in years but I was thinking what if you just sewed again around the edges of the chamois and then pulled out the original stitching?

I'm assuming you can see the "evil" stitching. I would use cotton-wrapped polyester thread. Matching colour for the outside and, in order to differentiate from the original thread, a contrasting colour inside.

If I remember correctly, when you sew stretchy fabric, you have to pull it a bit as it goes through the sewing machine. (Front and back at the same time so the part under the needle is taut).

It couldn't hurt to try, or explain to a seamstress what you're looking for, as they sound unwearable at the moment.

Good luck.