I was using mill drills to do some engraving on steel and aluminum. I learned how to sharpen these myself to get decent results. That is after the points get worn or chipped.
I still use mill drills when I have other operations to do with the same bit, but now when engraving or spotting, I just grind a drill bit. Probably not as good a solution for the smaller bits, but you should be able to use larger and grind them to a point like you need.
I use basically the same geometry as the original bit, but at a steeper angle like 82 or 90 degrees. HSS drill bits are less prone to chipping the points than carbide or cobalt especially using a router setup that may not be as rigid as a mill.
If the brass is clogging up your cutter, you may need to slow it way down on the spindle speed. I haven't done that much brass, but the little I have done was very easy. Better than aluminum actually.
You might also try air blasts while engraving to keep the point cool and the chips cleared. If you are using a router, it may be blowing air down already, but this is usually hot air after awhile.