Felt - tanned hide - any soft cloth will work. I think the tire inner tube is a great idea, probably the best because it also adds vibration dampening. None will effect the bow and all will help quiet it down. I will 2nd the brace height and think you should try twisting the string a couple turns at a time until it gets real quiet. Suggested brace height is just that, "A suggestion" and every bow will shoot differently. Even for different shooters and a perfect brace for you on one bow may not work for me. Draw length, release and arrow choice will effect it. Add something between the limbs and riser then play with you brace - all will be good.
Bob Urban