There are quite a few random image display scripts out there, but most of them are set up to only display a single image at a time.
Have you considered using an image rotator script, that will reload the "random image" at interval rather than trying to display numerous "random" images at once (seem to me that might be a little easier on the server).
If you would share a link to your attempt at using the alistapart.com method, some here might could help you debug it.
A note on the allow_url_fopen issue: As long as you are calling images from your own server (not from another site's web pages) you won't need to go to the bother of "cURLifying" the script as described in the wiki. You can just change the code that indicates the image file from "http://somethingorother.domain.tld/images/picture.jpg", or what ever, to just use the path to the file on your server (like "images/picture.jpg" or "/home/yourusername/yourdomain.tld/images/picture.jpg").
You can also avoid that whole issue by using a perl or python script instead of PHP. many perl scripts exist for this (many work in conjunction with SSI).
Was there a particular script that you liked but were not able to get installed?