Nothing can move quietly on dry leaves. Nothing.
I think the only thing to do is to move like a deer moves. You be as quiet as you can, but mostly you spend time stopped, watching and listening. We hear deer all the time as they move through the bush, but, if you watch them closely, they actually spend a LOT of time not moving. If you move like that rather than marching along like humans so often do, animals tend to wait until they can see you (or smell you, of course, but that's another problem entirely) before they move off. Behave like a deer, and lots of inhabitants will assume you are one until they know you aren't.
As for soles, soft and thin is the key. I have a pair of moose hide wraparound moccasins made for me by a woman in Isle-a-la Crosse when I worked there as a teacher, that I still use if I want to be quiet. They are not that great for walking long distances or for really rough ground, but for slowly moving through forest, they are very good. They hug my foot, so their footprint is narrow and they crush fewer leaves, and they allow me to feel twigs and things as I put my foot down so I break fewer. I think soft and thin would be my aim for a new sole. Bare feet, or just socks (we used to do that when we were kids and trying sneak up on things) would be better, but I'm just not that serious about it any more.