Success! I used MPEG Streamclip and converted my footage to QT .mov files, max quality, Apple DV/DVCPRO NTSC and the problem is resolved.
So much for just dropping the footage on the timeline! I haven’t tried this on a Windows editing system yet, but the MP4 issue is probably relevant there too.
Short story: Flip cameras require conversion to a more native/friendly format for the editing software being used. But hey, at $150, I guess you get what you pay for. 🙂
Thanks a ton to everyone for helping me resolve this! My school thanks you too!