how can I calculate pitch deviation in a large collection of audio files?
Use a very slow LFO to get very long segments of uniform pitch (this will allow you to use long analysis windows and counter 'border' effects), and use the simplest possible waveform for the oscillator to prevent octave errors in pitch detection. Aubio provides an implementation of the YIN algorithm which is fairly accurate.

I personally doubt there's anything fancy going on here - it is very likely that the relationship between the LFO modulation depth and the pitch deviation in cents is linear.