I don't believe the pins should have detectable play -- the floating part of the caliper should move smoothly in and out only.

Are the pads uniform thickness or are they tapered? If tapered, you definitely need to replace the pins (and pads).

Just use the sandpaper to make the surface of the rotor matt in appearance. Fastest to use an angle grinder with a coarse sandpaper pad, only takes a few seconds that way. Otherwise, the brakes groan.

Check for even pad wear on each axle, inner and outer -- if you have a bad brake line or sticking caliper, some pads will be thicker than others -- it's normal or either the inner or outer pad in a caliper to be thinner, but they should be the same as on the other wheel.

Peter

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1972 220D ?? miles
1988 300E 200,012
1987 300D Turbo killed 9/25/07, 275,000 miles
1985 Volvo 740 GLE Turobodiesel 218,000
1972 280 SE 4.5 165, 000 - It runs!