brake pads won't fit

If you sand the pads, then get some of the mesh drywall sanding sheets from any harware or building supply store, in a grit like about 180 or 220 and with the black type of grit. Place the grit mesh on a very flat surface and work in a circular motion and reverse the pads every 10-15 seconds. I sand the racing pads lightly on my rally cars to get a fresh surface and never, ever have an issue.

BUT in your case, 2mm is .080", and that is a LOT more than I take off. So either the pads are wrong or the pistons are not fully back, as said.