Hmm, my only complaint about ignoring overflow is that, after enough lead and anything else you may want to hit it with has been slammed into the SOB, you're going to get to a point where there isn't much of a body left. If you've hit max overflow, the corpse will not even vaguely look like it's original shape, get over twice the max overflow and you're going into "bloody smear" territory.
The problems that i've seen plague this discussion so far is not one of what rules apply, but more of if people choose mechanics over realism or vice versa...
If, by what has been said in the previous interpretations of the rules, you get the sod to deadly damage, i'd say you got the bugger on the ropes, either which way you are looking at it, any further damage is going to seriously inconvenience any regenerating attempt (after all, overflow is just to simulate even more deadly and horrific damage to whomever is unlucky enough to be said situation). Somebody hacking blindly with a Katana at what is essentialy a near corpse is going to get to the point where there isn't much left to cut anymore. Similarly, someone hosing down someone with prolonged and sustained firepower is going to get to the point where there isn't much left to shoot.
Now a vamp could still regenerate this damage, in games mechanics terms, but from the point of realism (and yes, i do know that this is a game set in a fictitious world and that pretty much anything can and will happen) where do you get to the point where there simply is not enough vampire left to regenerate? Does reaching body overflow at least count as "extensive tissue damage"? (i'd say a big "hell, yeah!" to that).
As per usual, SR3, nor any sourcebooks, gives a hard or fast rule on the subject, leaving a wonderful vista of grey area before us. (I personally think they do this so that we can whittle away our time arguing about it in forums like these, but then, everyone has got to have a hobby..

)
My only opinion is to try and use common sense where applicable (OK, i realise that this is Shadowrun we're talking about, but one remains optimistic, despite my natural state of being an apathetic pessimist (or is that a pathetic pessimist? who knows?

)) i will say this though, no matter what you decide is best for your game, keep them regen rolls a secret and do them at the begining of the combat turn, YOU (as the GM) may know the SOB's dead as a door nail, but the players don't and there's nothing i love more than to see players sweat...
As for my contribution to "What are we hitting the vampire with?", i'd suggest a vindicator minigun or HV weapon loaded with splash rounds containing Green Ring 8. It may regen the damage, but it's not gonna be thinking about stomping your ass when it's puking it's guts up...
That's my tuppence worth anyway, hope it made sense!