Before you grind anything, are they Ferodo Platinum pads?
Maybe change them to something else just to see what happens.
I had the same squeal, the kind that makes school children wince and put fingers in their ears, with the Platinum pads under light brake application on a rotor that I blanchard ground the chromium plating off of until it was dead balls parallel with the mounting surface. I have a suspicion the pads are not my only problem since the original pistons were still fitted and we all know how weather resistant they are after 35 years of no dust boots.
Just saying, try to find an obvious issue before resorting to any grinding. GRINDING CANNOT BE UNDONE without replacement.
The stock caliper doesn't float to take up any warping but since it has opposed pistons they can float without greatly influencing the feel if there is any axial runout as long as both disc swept surfaces are parallel, so warping is not super critical for average use within reason of course. Indicate both sides and mark them with a sharpie as you go along so at least you know the disc condition when mounted. If the squeal sounds like a cheap motel bed late on a Friday night then disregard the above and have it cleaned but that should be noticeable in the hand lever without the bother of indicating.
Brake squeal can be an sob to mitigate and what you really end up doing is moving the resonant frequency to a range that the human ear cannot perceive. But try the easy things first. Make sure both pistons are free to move, grease the backings, then try some of the anti-squeal shims, I made my own from a kit that was big enough to cut up. Use the scientific method, one change at a time, and please report the findings. My shims made no difference at all.
My unit is still up on the table since the new caliper pistons (and many ongoing reliability / maintenance items) so I have nothing to report as yet.
So, what are the pads?
All the best.