First off, Congrats on the new ride.

Yes, you do have a Paramount track. Sounds like early to mid 90's. I have one that is red and yes, it does have the Cinelli BB. Mine is on the fixed gallery, http://www.fixedgeargallery.com/2004/aukerman10.htm. The bike now has a chrome straight blade fork (Colnago knock-off). I have seen a couple of Paramounts that match the description of yours and they were pretty cool point jobs. Definately leads a custom paint air to it all.

Again, congrats on coming across the 'Mount. Post pics when you get a chance.