My computer build now includes a piece of structural 8.5x11 printer paper.
I tracked the tapping noise to the case fan, poked at it a bit, and realized it got perfectly happy with just a bit of upward support. So, a bit of bridging between that and the top of the card cutouts just below, and I have a near-silent computer again! (Ignore the dust, that's the next task.) #lowtechtech
I do want to take a deeper look at what's going on eventually, yeah. It's one of the fans built into the case, though, rather than something I added during the build, so I'm going to have to see how easily I can remove it in the first place. I love the space and the wire management this case allows, but its parts are more tightly attached (if apparently not tightly enough in this case) than others I've worked with in the past.