What you are trying to do is wear the pad buildup off the disc.
Why do they squeal (and feel grabby) and even more so when wet? Just my theory but I think water acts as an imperfect lubricant and you get the same effect as running your hand across the top of a glass that has been lightly moistened; vibes you hear and feel through the controls.
My Ducati's Brembos are fussy about this. Working a 3M pad or higher grit (say 220 or 320) sandpaper around the rim will sometimes work to reduce the noise but ultimately pad material will attach to the disc again and I'm back where I started, sometimes within the space of just a few miles. As has been said, a few hard stops will temporarily reduce or eliminate the effect. When the discs have built up pad material, as they seem to around town, I find that the noise is most obvious towards the end of a stop when I'm easing up on the brake pressure.
My Evora doesn't elicit these symptoms, but my Ducatis all seem to and will clean up with a bit of hard scrubbing but will come back again in short order. I'm still on the original pads on my Multistrada so not much has changed but my riding buddies tell me that a change in pad material will often result in a change in the squeak quotient.
That said, squealing is often an indicator of pad wear and many street pads are intentionally fitted with an element that will cause them to squeal once the pads are worn past a certain point.