Poisoned *and* Stabbed?

We need to discuss more play topics.  I've been poking around my other site Shakespeare Answers, looking to see some of the most popular questions.  What follows isn't one of the questions, but it got me thinking :).

Hamlet both poisons and stabs Claudius.  Why?

If you stab somebody and he doesn't die - stab him again, no?

In some interpretations Claudius is merely wounded ("O, yet defend me, friends; I am but hurt.") and then Hamlet forces him to drink the poison at swordpoint(?).  In an interpretation like that it seems as if Hamlet's calm cool and collected (albeit a little insane) and is definitely thinking of providing a suitable ending for Claudius, now that he's got him cornered.

But it also seems equally plausible that Claudius is already mortally wounded by Hamlet's envenom'd blade, and a clearly insane Hamlet has to hold him up to pour the poison down his throat.  If he'd just waited a few seconds maybe Claudius would go on his own.  So, as noted - instead of stabbing him again, he opts to poison him some more.  Does that make sense?

I've always taken the position that it's that "Follow my mother!" line that tells us all we need to know about Hamlet.  It's revenge for her, not for his father, that finally spurs him to act.  The whole "Dude, you're dead and you just haven't fallen down yet, give it a second" revelation by Laertes certainly helps shift Hamlet into a "Now or never" mode, but if you take out Gertrude's poisoning, would the scene have gone down the same?  Would being mortally wounded himself have caused Hamlet to finally act?  Or would he have gone to the undiscovered country still talking about it?