To address the "Pinching", that's why I said to put the rings about 3-4 inches back from one edge and sew them in place. That material would address the pinching concern.
I had considered tubing, but I have heard that you need a wide band of some sort, that a narrow band of what ever sort can damage the flesh because it needs to be so tight. I don't know if there is any substance to this or not, but figured why take the chance.