Boyle already ensured it would rise to that altitude and stay there. A slow leak would work, even by diffusion though the balloon envelope and Boyle might see to it that there was a slow return.
It could be from 12 to 24 miles up; If it's at the higher end of that range one will need a really good gun for a fighter to shoot it down. Then there's the rounds falling at random back onto Montana. The density may seem low, but it's sure one will hit the most valuable cow in a herd. Missiles are also a problem as the target one really wants is the balloon, which has not much radar or thermal signature. I checked and the air density at 120k ft is 0.002 that of sea level. Maybe that helps with the rounds from the fighter having less drag?