Determine angular position from two potentiometers
There will be a gap in each of the two pots near where they (ideally) instantaneously switch from 95% to 5% or vice-versa depending on the direction of rotation. 

I suggest using the center range of each- switching from one to the other when the current one goes out of the center of the range, in this case it would be 50% +/- 22.5%. There will tend to be a smallish glitch at the transition. If you need to eliminate that you could blend the two readings together with a function that weights the two readings in a variable fashion. You still want to ignore the output that is too close to the transition, but to blend the two inputs in the intermediate range.