Alright, so I was bored and started turning wrenches.
I think I've found where the clunking is going on: the spherical bearings are held in place on top of the control arm bolts, by what I'll call 2 metal bushings each. They fit over the bolt and make up the gap between it and the bearing, like a normal rubber or polyurethane bushing would.
What's happened is I think these are not a snug fit over the bolt (either by design or because of wear, but I'm guessing by design), and as a result they're dirty and have too much clearance.
They're still functional, but now I see I need to replace them and find a way to prevent this from happening in the future. I'll probably get with BMR and ask what they recommend. It may just be that I need some new bolts. It may also need some kind of lube, but I don't see how you would service these without complete disassembly, and the lube wouldn't last forever because this is all an open design.