I could use a lookup table to solve my linearity issues, but...
Perhaps I should have been more specific with my initial post. My desire to have a linear relationship between digi-pot setting and output voltage really stems from two main reasons. The first being that it will simplify my code, but the second and arguably more important reason is to maximize resolution.
If I were to find a way to make the relationship linear using a 256 position digi-pot, then the resolution of output voltage I could expect would be somewhere around:
[LATEX]\frac{10V - 1V}{256} \cong \pm 35 mV[/LATEX]
If I don't find a way to make the relationship truly linear, but use a lookup table to make it approximately linear by essentially skipping over some positions within the digi-pot, then the maximum resolution I could hope for would be equivalent to the largest change in Vout between any two digi-pot positions.
In my case using a 30 kΩ digi-pot, the largest ΔVout occurs between positions 0 and 1 and is about 750 mV. That's not enough resolution for me unfortunately.
I'm still trying to crack this nut.