If you're already consulting a podiatrist, then you're getting way more info from him than you will from me. Still, my two cents:
Is there a reason that you're only riding Burton boots and bindings? Have you tried other brands since your problems began? Each manufacturer is going to use a different last, and that might be your issue. Burton's last may be particularly ill fitting for your feet.
I second the idea that you should try aftermarket orthotic-type insoles. The ones that come with your boots are pretty crappy.
I'm curious about where in your foot the pain is. If running your feet helps, it sounds to me like a potential pressure point issue. Again, that makes me think that you're wearing poorly fitting boots.
The last option is that you may have some type of physical injury that needs to be addressed. If you're having the same pain in both feet, this seems less likely to me (though not impossible)...