It is fixed. The whole time it was an exhaust leak. It didn't sound like any exhaust leak I had ever heard though, and multiple mechanics had listened to the noise as well and thought it had to be something in the head. Anyway, we pulled the manifold gasket out and it had some discoloration where it had been leaking.
I bought a new gasket from CarQuest and it was significantly thicker around the ports than the gasket that came with the kit I bought.
So anyway, as soon as we replaced the gasket and torqued the bolts, NO MORE NOISE!!!!!
Keep in mind I did this proactively, so I was really frustrated when I thought I introduced an issue that hadn't existed before. Thanks for all your feedback throughout. Great forum!