After installing new calipers, due to seized pistons, my front brakes have been squealing like crazy to the point of making it unpleasant to drive. Here's what I've tried so far.
Bear in mind that I'm re-using my old pads, so pad composition is not the issue. Copper slip on the back of the pads. 3M stick-on shims on the back of the pads. These seem to be pretty much useless and they just don't stick. New pad clips. Chamfering the leading edges of the pads.
Currently I have removed the shims but used some of the off-cuts to make liners to sit between the pad's metal edge and the caliper itself. In the photos you can see where the pad's metal backing plate rubs on the caliper either side of the disc. The only issue with this is that it makes the pad tight top-to-bottom in the caliper, so making refitting the pads difficult. Not tested this yet, but I'm hopeful.