Your naïve interpretation of the work equation doesn't quite make sense in this context.  Consider that the standard formula for work gives that $W=\int {\vec F}\cdot d{\vec x}$.  At minimum, the presence of the dot product in the above equation should not be ignored, and we should interpret, for a radial force, the work to be equal to $\int \frac{F\,dr}{\sqrt{1-\frac{2M}{r}}}^{1}$.  We should then note that this factor will exactly cancel the effect you cite.


${}^{1}$Note that the measure of the integra $\sqrt{|g|}$ has a factor of $\sqrt{1-\frac{2M}{r}}$ that cancels against the factor of $\frac{1}{1-\frac{2M}{r}}$ in $g_{rr}$