And after a couple of weeks playing with trial versions of Adobe Premiere Elements, Cyberlink PowerDirector, Pinnacle Studio, MAGIX Movie Edit Pro, Corel VideoStudio Pro X3 and Sony Vegas, I declare the winner to be:

Sony Vegas

The others all crashed, some even while not actually doing anything. So far, Sony Vegas has done everything I've asked of it (which is, admittedly, not exactly James Cameron-level), and hasn't hiccuped once.