A fine, white rouge on a buffing wheel is the best and quickest way of removing the scratches, and also to get a mirror polish.
At HF, I bought a mounted buffing wheel and a block of the finest rouge they had in stock, which is usually white. I have never had any success with the red and brown rouges, and the black is course, for heavy cutting.
A mounted wheel is just an arbor that fits in the chuck, and you attach a cloth wheel to it. A diameter of 4 to 6 inches is sufficient. Mount the buffing wheel, turn on the lathe, touch the rouge to the spinning wheel to get rouge on the wheel, and polish. The rouge slings off, so you might have to apply the rouge several times to polish a cartridge case. I run mine pretty fast--2 to 3 thousand RPM.
You can also mount the arbor and wheel in a drill press.
The brass I have is old, with a lot of tarnish. I insert it in the lathe chuck and polish with 220 grit paper, if it is really tarnished and scratched, then go to 400 grit paper. If in fairly good condition, with just discolaration, I start with 400 grit paper, then use the buffing wheel. The buffing wheel and compound will remove the 400 grit quickly, leaving a mirror polish.
I have used the mounted wheel and white rouge to polish stabilized wood and antler and the PR blanks. It will also polish fine sanded wood pretty good, but the shine is only temporary. Do not use anything but white rouge on wood. The red and brown will get in the pores of the wood, making an unsightly mess.
If you are inclined to do it, the buffing wheel will also remove the gold plating from the metal parts, leaving a smooth finish.
Hope this helps.
Bonefish