Had my rotors machined and wheels balanced yesterday. Hoping this took care of the shimmy, but I'm not 100% confident it will. I still think there's a caliper pin sticking. But we will see.
I had asked the mech to also look at the caliper pins, but he's pretty confident that these two fixes will take care of the problem, so he didn't take apart the calipers yet. I guess I can't complain, because he didn't charge me anything for the work he did.