My thoughts? Don't bring the dogs.
Griz are very different animals than black bears. Blackies are far more tolerant and far less aggressive. 99% of the time, a griz will run the other way at seeing you. However, the possibility for a dangerous encounter is greatly increased with griz. Black bear sows are known not to attack even when their cubs are being trapped for tracking purposes. Griz--not so much.
We don't need to get into the whole "Bear Danger !" discussion, but you are dealing with a very different animal. A dog would most likely exacerbate the situation exactly when it needs to be de-escalated.
Also, read Bear Attacks: Their Causes and Avoidance by Steve Herrerro. He's a professor emeritus at the University of Calgary and spent a career researching bears and their behavior.