Wow, some expensive grouse here!
My forest grouse hunting is almost always with a rimfire - and the bulk of that with a pistol. Doesn't matter much which ammo....just use what's most accurate. Aim for the head if it's convenient, but don't sweat it if it's not. Just about everywhere I might shoot a grouse, there will be some kind of backstop in case I miss (which is rare, since the shots are usually easy ones).
A dot sight helps when shooting under thick forest in bad light.