Syllogisms in Logic Classes: the "Existential Fallacy"

When I took logic back in college, we did not go into that much detail, so I would like SylloGizmo users (I see there have been 70 downloads already) to tell me how the issue is being covered in their classes. I refer to the issue sometimes called, "the existential fallacy", i.e., the fact that without a "strengthening premise", the syllogisms Darapti, Bramantip and a few others are not valid: unless elements of both classes actually exist, the conclusion does not follow from the premises.

Now my primary source on Syllogisms, Quine's excellent book "Methods of Logic" has a logically simple way of dealing with the issue, but I do not see the same language being used either on Wikipedia or anywhere else on the web. That is why I am asking you users: do your classes/texts use the same approach as the Wikipedia article? As the Friesian article? Or do they dismiss Darapti etc. as invalid with no further discussion? Do they even discuss the difference between propositions as descriptions of classes, and as descriptions of properties?

BTW: one of the curious differences between Quine and all these other sources is: his list of premises valid with a strengthening existential premise is bigger. Wikipedia lists only 4, but Quine lists several more, i.e. AAI-1, EAO-1, EAO-2, AEO-2, and AEO-4.

I am sure Quine is right, these too are valid; my guess is that others left them out because they are too trivial.