For reasons that others can probably explain better than I can, bicycle shoes, i.e., designed for biking, really do make a big difference! They are stiffer so that you are using the foot more efficiently plus it is not flexing so much. I have to be kind of careful with my feet due to very high arches and other things, and I also use orthotics in my bike shoes; others here have mentioned things like 'buttons' behind the ball of the foot. My first shoes were some relatively inexpensive MTB type shoes which you can put cleats into, but would not have to. You might give biking shoes a try.
The bicycle is the most civilized conveyance known to man. Other forms of transport grow daily more nightmarish. Only the bicycle remains pure in heart. ~Iris Murdoch, The Red and the Green