I wear Brooks and Asics sneakers, Softwalk and Drew for dress shoes- womens. I cannot feel my feet at all so just buy a size larger, 13's. I tried wide shoes but couldn't drive in them since I have limited feeling in my legs, it just seemed like the wider shoes got caught between the pedals.
Drew makes mens' shoes too, have you tried them? They are all leather and very smooth inside, with a double depth option.
This probably isn't encouraging but I really don't think shoes make a big difference in the burning for many of us. My favorite shoes are Finn comfort sandals. Very pricey but they do not irritate my feet at all.