What I have done in the past, is to chuck that drum in a lathe,and spin it up slow.You can rough-cut a few thou off. Then with an emery-cloth role and a lathe-file, shave it down.Start with a coarse cloth(80 to 100ish) and finish up with maybe 240ish. That and a new band and youre good to go. Youre only gonna smooth off the worst of it. Dont try and cut/grind the deepest gouges out, thats kind of a waste of good metal. For a street car the band wont see the loss of surface area. It will however,one day in the far future,notice if you smooth the drum down to a significantly smaller diameter.
-As to the piston, I cant get a sense of how much damage is there.But there is a steel sitting next to it, so it shouldnt be an issue.As long as the center register is smooth to seal oilpressure, and the plate side is reasonably flat, and its not cracked, it should be fine. Bear in mind that it spins at or near to crankshaft speed, so if its not real flat you might consider chucking it in a lathe and take out the worst of the high spot(s). A little bevel on the largest diameter of the face would likely be better than cutting the whole thing down if its gonna take a large cut.Also consider that any material that you cut off the face will directly affect your total plate clearance. I used to work for a commercial rebuilder that would routinely cut that plate thinner as well as the pressure plate on the outside of the stack, to help in installing an extra steel with thinner frictions. Voila, extra load capacity.
-Hope that helps