Well, your one suggestion might work -- I'd say, collect all the things you want to save, and then compress them into a series of zip files....say...30 meg pieces? And then transfer them to someone. After he/she recieves each piece, check to make sure they uncompress ok.

Continue to do that until they've got all the pieces transferred...when you get your new computer, they can just send it back, or, if they have a CD writer, perhaps they can burn the stuff to CD for you?