I found the source of the noise.
It was in fact the crossover pipe heatshield on top. And specifically, it was the passenger side half that had one of those two bolts sheared off at the head. Thanks for the suggestions and pictures. The only thing remaining was a tiny bit of the threaded portion, but enough to keep the washer in place. Sort of. The washer wasn't tightened down onto anything, but couldn't just fall off because a bit of the broken bolt had stopped it from coming out on its own. It was plenty loose enough to rattle though... every time you hit the gas.
I got the washer out of there and put a hose clamp on for the time being. That is not a nice area to gain access to from above, so once I get some time to get at it from underneath properly, I'll put a couple hose clamps on and make sure they're good and tight and well centred. In the meantime, it stopped the vibration noise. I went out for about a 30 mile drive and the car drove real nice.
I'd say it was a big relief to get it sorted out, but I wasn't really all that thrilled about it when I finally tracked it down. I probably just muttered asshole to the car as I shut the light off in the garage and went inside.