<... Since the spring rate is an absolute value that is unaffected by ambient pressure and the area of the valve face is fixed, I can see no mechanical reason why this shouldn't work ...>

The pressure trying to OPEN the valve is MAP applied against the inside face of the valve.  The pressure trying to CLOSE the valve is spring tension PLUS ambient pressure applied on the outside face of the valve.

You will have to somehow compensate for the ambient pressure outside the valve ... Jim S.