Potentiometer output voltage deviates from calculated value as knob is turned away from 50%
The electrical angle is typically considerably smaller than the mechanical angle. The number for electrical angle is not given in the datasheet for that pot (which appears to be an obsolete Panasonic EVN series). The datasheet specifies the mechanical angle as 210+/-20 degrees. That means it could turn as little as 190 degrees. 

I have opened one up so you can see the actual electrical angle. There is a highly conductive material at the ends which marks the ends of the electrical angle. When the wiper rides up on those ends, the resistance is typically only a few ohms (the "residual" is maximum 300 ohms for the one you have), and it no longer changes significantly as the wiper is rotated through the overtravel. 

As you can see from the below microphotograph of the unit I dissected, the electrical angle is very close to 180 degrees. So a curve of voltage vs. angle will be flat at either and and will go from almost zero to almost 100% over an angle of about 180 degrees.  



That is why, if you ignore the one or two measurements near the ends, you will see a consistent steeper angle than the average of all the points. 

A secondary effect, which could be measurable with a 100K pot and 10M load is that the curve will be steeper near the center of the rotation. You are unlikely to be able to see that with a tiny trimpot without some very fancy equipment to manipulate the wiper, but it is real. That is because the Thevenin equivalent source resistance of a 100K pot varies from almost zero at either end to about 25K at the center of rotation. The loading from the 10M will result in a droop of a fraction of 1% (about 0.25% of unloaded voltage) at the center of rotation. This is too small to worry about with a trimpot, but in some situations it can be important.