I think I have arrived at the answer to this question.
The problem is the single point I was drawing to set the scale of the polar plot. Even though I was drawing this point before setting the colororder, MatLab was counting that draw when assigning colors. Since this point was not included in the colororder, this had the effect of shifting the colors for all the subsequent angles. Since the two plots have different separations between points, the change in color at each direction will be different.
I had thought that setting the colororder reset the draw count, but this does not seem to be the case. My issue can be resolved by simply including a dummy line in the colororder for the plotted point.