I have been grinding nothing but brisket for burgers for a couple of years now. I don't make a lot of them at once because if I do, I'll get a grease fire for sure. Not a flare-up, a CONFLAGRATION. So I just use all the fat. One thing I do that cuts down on the mess is that I cut up the meat into domino-size chunks and lay them out on a cookie sheet and freeze them for 30-40 minutes to firm them up. Stops all the spattering when grinding.
Brisket burgers are wonderful. Flavorful and juicy for days ..