Now you lost me a bit. Going pear shaped would be an indication of square (computer) vs rectangular (TV) pixels, a bit different issue than posterization. You also point out that the movies look OK in QuickTime... did you use QTPro to create a slideshow? And then bring this slideshow into iMovie? In other words, what is your exact workflow and how does it differ from your friends?
And we may also want to back up a step. Strictly speaking, I am not sure you would be happy with FCE from an image quality standpoint. If there are other things you are looking to accomplish with an editor and iMovie is holding you back, then I wouldn't hesitate to say jump to FCE. I took a quick peak at the website and personally, I think you will be better of just biting the bullet and getting Adobe After Effects. Here is a quick tutorial with After Effects and a slideshow:
http://library.creativecow.net/articles/kramer_andrew/slideshows.php
And again, this rendering engine will be superior to even FCP. I have two other quick suggestions. One, I wouldn't use a cross-dissolve transition between slides. I personally wouldn't use any but a cross-dissolve is very hard to compress efficiently and will almost always break up when compressed the web. The 2nd would be to add a slight key-frame to each image. Even if it's minimal, slight motion helps eliminate a lot of artifacts presented when using motion picture platform (video slideshow) with still images.
Mike