Third (and best, IMHO) would be to run separate FastCGI processes for each customer, and route appropriately from Nginx. This approach is obviously the most complex setup, but it has the major advantage of letting you run every customer's FCGI backend under a different user id, offering yet another level of protection against data leakage and other security issues.
I like the third option quite a bit (though what I was trying to do looked more like the second) but the problem that I'm having moreso than anything is in trying to GET a fastcgi parameter as a variable in my settings.py.
I'll carry this over to SO, as the downvotes suggest that this is not only offtopic, but inappropriately placed altogether, but thanks a million for your insight.
The other advantage of the third option is that you don't have to write a whole bunch of auth/filtering code to only show customers their own data. Row-level permissions are relatively straightforward in Django, but it's still easier not to have to deal with them.