I noticed that every once in a while, when I'm coasting in neutral to a full stop, the auto-stop function will cut the engine... Good... But it doesn't seem to fit with the conditions in the manual-

so what are the criteria for a neutral auto-stop on the HCH?

Mine never autostopped in N. But I don't use N anymore because you get just as good a FE boost by letting off the gas, but not completely, so that you enter superlean mode - FE skyrockets until you accelerate again. I found it to be just as effective, if not more, than using N, plus no worries about putting it back in D before you stop to preserve the autostop feature.

On this board there has been significant discussion on the use of N, but not for a while so if you're new you might have missed it. Searching back 6 months or so might turn up some of the debates. I think most concluded that using N was unnecessary because of the lean mode you get by backing off the gas, some even suggested that N wastes gas because you're idling without being in lean mode, though there was never any significant evidence produced - mostly people's interpretations of what they think the car is doing.