With the exception of FITASC, I shoot pre-mounted most of the time. This works great for me. I like pre-mount because it allows less room for error. With proper coaching of the technique you can actually shoot the targets faster in the proper place and there is no rush to mount the gun.
However, on occasions, such as a fast target, I'll start with my gun just out of my shoulder, so that the movement of mounting helps generate the extra speed of swing required to sustain the lead I need to kill the target.