You'll have to be more specific I think. Where does it hurt when going toe-side? Sounds weird. Have you tried tweaking your bindings on the hill by small amounts? Go for small angle changes and try a run or two. Like you say, when you are standing your feet are 'turned out' more than the angles you have set.
I stood at approx stance width and angled my feet out til it felt right to squat down, like my knees and everything were in alignment and comfortable. That gave me a place to start.
Go back to looking at some youtube vids of how to set up bindings for your height and favoured stance perhaps?
I ride a 158 and am 5'11", my bindings are centered on the holes and it feels perfect, not too wide or narrow. 6'1" on a 156 doesn't sound crazy but if anything centered could be a bit narrow?
Hope that's some help!