On my previous Skyrim installation, I removed the compass by changing a simple value in the skyrimprefs.ini file. Now, after a clean install, I don't see that option anywhere in the ini. There simply is no ShowCompass toggle to change from 1 to 0.

Any ideas?

It ought to be in the [Interface] section of your SkyrimPrefs.ini. But if you don't see it there, copy/paste this line:

bShowCompass=0