Pim, Serry, you're right, the promo video has the same stand alone-version as performed on the Maurizio Constanzo Show (only difference being that the latter is an instrumental version). I overlooked that. Thanks.
However (in reply to Serry), I'm positive that the Happiness-single does NOT have a stand alone-version. When I say stand alone-version, I mean a version that is REALLY disentangled from the song it segues into (or segues from) on the album. Such a version must be specially prepared.
Now the version of Happiness that appeared on the single is identical to the album cut, except that it fades out very abruptly (but if you don't want to use the term "fade out" in this context you can just as well say "ends) before "Revelations" starts. But if you listen closely enough, you can even hear the first noises of the segue into "Revelations". They obviously didn't prepare a special stand alone-version for this one and it doesn't differ from the album cut in substance. The promo video version, however, DOES differ substantially, as the outro is, as you said yourself, notably extended.
However, I should probably pinpoint that I used the UK CD Single as reference and therefore can't rule out the possibility that other formats of the single have different versions (though I think that's highly unlikely). I used to have the coloured 7' but sold it a while ago (which I've come to regret, it being a really nice item), so I can't check. I never managed to get hold of the 12' pic disc, which seems to be quite scarce these days (presumably because it belongs to the group of collectables owners very rarely sell and even tend to keep when they dissolve most of their collection...no wonder, it's all a collector could desire. Beautiful Picture Disc and a bunch of great bonus tracks that can't be found on any other record).
PS: I know that Jason was on stage that day and no, he didn't play live.