"My biggest problem is not with the foot slipping off it's with large thick soles hanging or bumping the edges of the pedal when I apply the brakes."

That's exactly the problem I've had on four different occasions: shoes with large thick soles catching the adjacent pedal. The last time this happened to me, I was preparing to cut a sharp right to pull away from the curb with a car parked ahead of mine (not terribly close; I had plenty of room––or should have had); I found my car easing forward but just a touch too fast; I went to move my foot from the gas to the brake, but found my foot (shoe) tucked UNDER the edge of the brake. It took a split second to get my foot out, up, and onto the brake, but a split second was all that was needed for my car's front bumper to go "Bump!" into the other car' rear bumper. Another shining moments in the lives of us folk with PN!

Have you ever seen the sketchers that have bumps on the bottom for better gripping the pedals without the larger soles you’ve described. In addition I find them really comfortable for walking. However, not all sketchers have this type of sole.