Results:

It worked, for the most part.  Here are the four saturated absorption spectrums I observed.  All but one of them yielded the expected results, except for one (85 Rb F = 2), for which the laser line width was slightly too big to distinguish the peaks.    The 87 Rb F = 1 spectrum has a crossover peak that is negative, indicating that more light was absorbed in the probe beam.  This remained a source of mystery; normally there would be a positive peak in exactly that location.  Papers on similar experiments did not report the same feature.  The rather large uncertainty in the frequency scale is due to the random walk behavior of the OCTDL (on the order of 100 MHz over a few minutes), which made it difficult to calibrate well.  Unfortunately, this produced most of the uncertainty in the measurements as a whole.

(solid line is data, dotted line is fit.)