Since this thread was from last Saturday, the point may be moot, but I'm sure someone is curious.
I grill BSCBs quite often. I always brine them, from a simple salt/sugar/water brine, to a more complex brine using orange juice and a little curing salt. The brining denatures the meat, allowing it to hold more liquid.
I grill them one of two ways. Now, here's where I decide how I'm going to prepare and grill them.
1. If they are all big and thick, and relatively the same size, I brine them for 12-24 hours, then grill them direct over high heat for 4 minutes a side. Then I move them to the indirect side of the grill, sauce them, and let them go 4 minutes a side, closing the lid, flipping and saucing as necessary, until the IT of the thickest part is 165F.
2. If they are different sizes, which is usually the case, I pound them with a mallet until they are about 1/2" thick. Then I brine them, usually only for 4-6 hours. Grill them over direct heat for 2-3 minutes, flip, sauce, then move to the indirect side and sauce again. They only need another 2-4 minutes a side until the IT is 165F.
Now, here's the key to getting accurate IT when you sauce BSCBs, especially with the pounded version. Make sure your sauce is hot. DO NOT use cold sauce. It will mess with your IT and you'll end up over-cooking the breasts. Trust me. Took me a long time to figure out why I was overcooking my sauced BSCBs.