Hi jags,
Can you tell me a bit more about how you cleaned your rims and pads? Sometimes, if soap is used, a little left behind can cause a terrible squeal. In that case, a simple rinsing with clear water helps. Other times, just cleaning them (at all) can do it.
I've run into this occasionally myself, and decided to make a study of it, 'best I could, using a borrowed camera that takes high-speed/slow-motion video. I've concluded brake noise is usually caused by high-frequency judder -- the pads catch-and-release under pressure, rather than with a controlled and steady amount of slip. It seems to be caused by the rearward edge of the pad "stubbing its toe" on the rim, wedging in and then springing free, setting up an acoustic resonance with each cycle. The sound is just a side effect of the process, but a welcome one 'cos it alerts you to the fact you're not getting full and proper braking. Really clean pads and rims set-up the whole process anew by changing the coefficient of friction between pad and rim. When dirty, the rubber on the pad can "slip" a bit, even if toe-in is marginal. Clean it all up, and the rubber-pad interface gets "sticky" again and the pad and its mount can judder back and forth under braking and produce that awful squeal. I think this is why riding in the fog can sometimes produce a squeal in brakes that are quiet in the dry. The moisture changes the friction coefficient (amount of slippage).
My suggestion -- till a little pad-rubber can redeposit on the rims and the rims can re-oxidize a bit -- is to add a bit more toe-in. That has done the trick for me.
When Kool-Stop salmon pads of recent vintage are first installed, they have a little kick-up at the rear that helps set toe-in for you. After they've been worn a bit, that goes away. To help set toe-in on used Kool-Stops, I have small strips of plastic in 1mm, 1.5mm, and 2.0mm thickness I can use alone or stacked to get the toe-in I need. After cleaning, I've sometimes used the 2mm strip under the back of the pad when re-setting toe-in, and that does the trick. Some people use a thick rubber band wrapped around the pad to set toe-in, but that hasn't worked well for me; too squishy. I've had good luck with a business card, folded as necessary to achieve the needed thickness. I also have a special tool that clamps onto the rim that is supposed to do the same job and work on both sides at once, but it hasn't lived up to my expectations over the years, so I'm back to my little plastic strips or the folded business cards, which work a treat.
When possible, I first release the return springs on the brake arms when adjusting toe-in. That's one less thing to fight, and makes the job so much quicker and easier, especially with cantis or v-brakes.
I hope this helps, jags. Yes, that noise can be really something; enough to wake the dead!
Let us know how it comes out. If this doesn't work, there's other things to try. Have you checked the pivot bolts for tightness?
Best,
Dan.