One think to keep in mind is that in general, small U form factor cases are noisy

Yup. I'm quite aware of this, which is why I was asking about cases designed for this purpose. I've about given up, though, and might settle on a 2U rackmount case and replace the fans if they're noisy.

make sure there are some rubber spacers to help prevent case vibrations from using the desk as a speaker.

A very good point. I'll probably have to make some angle brackets myself for mounting the thing, so I should be able to figure out how to fit some thick rubber grommets in the holes that allow the bolt through to attach to the case and let the case rest on them. I figure threaded inserts are the right thing to use to attach it to the underside of the desk.