Haha, so basically I have big feet for my size. How sexy.
Would small bindings not fit a women's size 7 boot ever?
you could take the boot to a dealer and try the fit to see. The thing is that if the board is only recommended for small bindings then it is only so wide, so even if you can get your size 7 boot into a small binding the boot may be too wide for the board.
However you may find that if you put the size 7 boot in the medium biding and mount it on a board that is only supposed to have size small bindings the heel and toe overhang may not be a problem, it will depend on the board, binding, and boot combo, you would have to try it to see.
I suspect that your conditions in minnesota are similarly crappy/icy to ontario so you might eventually want a cambered board, but for a first board the easy turns and less catchy edges of rocker or hybrid might be a good start, and then you can flip your first board for another, probably at low cost if you buy used.
If you are buying used and are buying the board and bindings together try it out with your boots and see how it all fits.