Great thanks for the options. For option #1, what file should I edit? (Sorry I'm completely new to zenphoto.) For option #2, I think I'll wait until I familiarize myself with zenphoto a little more before upgrading.
In any case, it seems that the only overhead with random thumbnails is -- generating the thumbnail, right? Choosing a random (pre-generated) thumbnail is negligible in terms of CPU usage, right?
If so, then I should be OK once all images are pre-cached.