ddoyle,
If you have good temperature control during your case hardening, you can do it well below the 1700° F melting point of brass.
Experimenting with different materials will give you good experience. Go ahead and try some copper, brazing rod, and yellow brass, and see which works best for you.
I played around with brazing rod, some 16 gauge soft brass wire, and yellow brass scrap while trying to braze a trigger guard, a butt plate, and some ramrod tips made of sheet steel. For me, the 16 gauge brass wire was easiest to position and just the right amount of brass for the work. I could bend it and position it right along the joint which was handy with the butt plate.