Been watching to see if anyone with experience would pipe up. Still hopeful. As usual however, those of us without experience will speak with authority.
I'd do it. Just make sure your brother has a skookum back up rifle and the backbone to use it. Not like a friend of mine filming grizzlies with a back up when a bear charged. He got some great photos of the bear as it closed, hoping it would break off the charge, then stepped aside and knelt so his back up could have a clear shot. At that point he saw his back-up man running away with the rifle. (Fortunately the bear did stop the charge.)
As the biggest predator, a brownie should respond easily to a call. I've called several grizzlies, as well as blacks, and I'd be confident if I tried calling a brownie.
However, there are two problems with calling bears if you want to be selective in what you shoot. First is that if there is brush, etc. it can be really hard to judge a bear's size when it comes to the call. Second, and probably compounded by brownies, is that the bear may be so agggresive that you have to shoot it, whether it is the size you prefer or not. I've had female blacks with cubs come in to a call, and that could be a problem with an aggressive brownie.
You can hedge that in your favor by finding an isolated bear and looking him over before you set up and call. One you didn't see may still come in and complicate things of course.
As to a bow, its been done, and you can do it. Seems to me that Fred Bear or one of the men who did it used extra heavy arrows tuned to the bow, for max penetration. Shaving sharp goes without saying.
The probablilty is that the bear will run off when hit. If not, I'd want at least a .375 in cool hands. Forget shotguns and don't put faith in hand guns unless you are a very skilled and cool pistol shot.