Also check to see if you have a rust lip on the rotor. If you do then get it replaced or 'cut' off. This has been the source of my screech on my left rear for awhile now and it happens exactly as you describe. I don't know why the lip causes this sound but I will be replacing them this weekend. Also check for uneven or 'deep' grooves on the rotor surfaces these cause the screeching sound too.
A swap to stock pads did not help, the sound was not as loud after but still enough to erritate, I attribute the change to the new pad size more than anything. I just ended up with more dust
Hope this helps. Maybe someone should design a caliper that is not susceptible to harmonics when things go off a little