In my view, y high order polynomial is typically a "dumb" linearízation method in lack of a specifc physically plausible sensor characteristic. Respectively I would try to find a way to describe the actual characteristic with fewer parameters.
But I know that it's not always possible.
The 40 points table is mainly a problem of calibration effort. If you get good reproducibility by interpolating a limited number of calibration points with any kind of function, a possible solution can be to calculate the look-up table entries at calibration time. This brings also the advantage that the device firmware isn't restricted to a particular interpolation function, you can change it at any time as long as you have a sufficient fine table.