On the other hand, if I take "he's only three minutes late" as evidence that he did it, and "he's more than three minutes late" as evidence that he did it, I'm violating a principle of rationality.

If you take "he's just a few minutes late" as strong evidence that he did it, "he's quite a while late" as weak evidence that he did it and "he's early" as very strong evidence that he did not do it, this violation disappears.

I just thought of something else, too, that could explain why it took so long if the duel were short.

Suppose Hermione won relatively quickly, at around 12:05. H&C obliviates and memory-charms her, taking as much time as the duel he makes her remember, which could be several minutes. Then he has to do the same to Draco. At this point, it's around 12:15 or so, and the memory of casting the BCC would make it more like 12:16. Then H&C casts the charm himself and realizes he doesn't recall what time it is exactly. Decides to go with 12:30 because overshooting is way better than undershooting here and he thinks he'll be safe with 12:30, especially if he doesn't have much time before he goes zombie or something and can't just check the clock.

(Anyone notice that Quirrellmort seems to be living Life: The Interesting Parts Version?)

Even if the duel lasted only a few minutes and everything was over by, say, 12:10 or 12:20, that would mean Quirrel only waited six hours and 13-23 minutes, depending. Could even be deliberate -- an attempt to throw suspicion off himself by making the timing not quite perfect.

If by "not quite perfect" you mean "suspiciously close after the point that made observation with a Time Turner impossible", then yes, it's not quite perfect.