Thanks all ...

@Ray: I've read the help guide and the link, but I still don't understand what the "seconds" (numerator) refers to: in one possible interpretation it's 15x the value of another possible interpretation. Can you please show me the answer for that hypothetical example I stated?  That will resolve all ambiguity for me. Sorry if I'm being dense.  I'm guessing the answer is 1.0 × 0.9972695677 and not 15 × 0.9972695677 but I'm not positive about that.

@Brian: Yes, I've experimented with Orbitals, but the numbers it's populating into the ASCOM panel and therefore into the mount are not consistent with the comet's actual apparent movement. (I'm polar aligned to within a few arc-seconds of the pole according to SharpCap.) Conversely, the numbers it's sending to PHD2 for guiding seem pretty close to the "right" answer. But if I let it populate only the AP ASCOM panel/mount, and turn off guiding, the comet "drifts" in the camera field substantially, so much so that when enabling guiding, PHD2 has to work very hard to keep the guide star "shifting at the right rate", whereas (I think) the whole point of setting a shift rate in the mount itself is to accomplish the opposite (less corrections by the guiding system). The way it is working now is substantially worse than leaving the mount at Sidereal.

This is why I'm trying to understand precisely what the AP ASCOM panel is expecting and how that number is being interpreted.

@Todd: Interesting, thanks for the tip.