LabVIEW Calibration Routine
Ignoring the details of working through the 'unique' interface of LabVIEW, I would suggest using a simple  binary search algorithm. 

Set the pot to mid-scale, determine whether the null point lies in the lower or upper half of scale, then set the new upper and lower bounds, and repeat. 

Assuming your measurements are stable (you will have to program a delay to allow the op-amp to settle and probably you'll want to average some measurements) it will take one iteration per bit of the result. If your digital pot has 256 steps, it will thus take only 8 iterations to converge on the best setting. 

There are potentially faster optimization methods that depend on doing some calculations or that might be better dealing with a very noisy signal (for example fitting a least-square polynomial curve to a number of points and finding the zero), but I think this is more than adequate for the purpose. In fact you could do it several times and compare the results. 

This is really a special case of optimization where you are looking to minimize a cost function (the absolute value of the offset or the square of the offset), and with a fairly high cost of evaluating the function (since you have to wait a long time in computer terms for results). Fortunately, it should be fast enough to not be a significant time in human terms.