I realized that I can only hear this noise when playing loudly, and then I noticed this same noise, coming from the right channel again, on another disc with low bass notes. I got close to the speaker and determined that the noise was actually coming from inside the lower part of the cabinet. I pulled out the woofer to check for something loose that could becausing the buzz. Nothing looked obvious to me.
Thiel apparently uses twisted solid wire, for the woofers at least, which is very stiff. I slightly rerouted the wires around the driver to make sure they were no where near any part of it after it's screwed into the cabinet. This was the only thing I could see that could possibly be the problem. After I put it back together the buzz was gone!