Thanks to the help here, it's been determined that the mystery fixie of mine is a Centurion. Next question is: what's the seatpost diameter?

I recently bought both a 26.8 and a 26.6 Dura Ace aero post from eBay and neither seems to want to fit. The current post is shimmed and neither the shim nor the post have diameter markings and I don't have access to a caliper.

So, can anybody tell me what seatpost size I'll need? I'd rather not have to sand down my seat tube or the 26.6 post, nor do I want to go out and buy 26.4, 26.0, 25.8, and 25.0 posts and figure this out by trial and error...

Take it to a bike shop that has a seatpost sizer.
Or they may have several old posts of different sizes they keep on hand for working on bikes.