Ok. So I get new rotors, new calipers and I'm still hearing a
horrible squeeking sound from the front wheels.

I'm puzzled. I examine the bearings. All is OK.

I examine brake shoes. Correctly installed.

I take it into the shop.

They puzzle over it, fiddle with stuff, and then they test drive it
again. Without the plastic hubcaps.

No noise. Eureka!

The hubcaps are clearly the culprits. Turns out the combination of
the BFGoodrich ATs I've got installed, which are fairly rigid in the
sidewall, and the 0-5 degree C temps have conspired to create a rigid
plastic disc, which flexes slightly with compression of the sidewall
during tire rotation and makes a squeeky noise.

Any one else ever experience this? Any solutions short of waiting for
spring (another few weeks or so here in Victoria)?