Solved my own problem. It suddenly occurred to me that when I was trying to get onto the Allume/Alladin web site to investigate this, that I kept getting an error (I think their web site may be down or moved). What does that mean? It means that their web sire can't be contacted. Whats one of the Stuffit preferences? - Check for new versions, and of course that's trying to go out to the web.

Unchecked that in preferences (it's the penultimate tab, you may have to scroll) and now launching is instant again.