Thanks for that account and weblink, Robert. I recall reading something about the Kentucky sharpshooters' shooting match several years ago, but for the life of me can't recall now where I read it.
I think one reason why there is such a dearth of information about the "sharpshooter" role of the sharpshooter battalions is because, for the most part, they weren't involved much in siege or fixed-position combat. Atlanta and Vicksburg are two exceptions. In the final stages of the Vicksburg siege, the 12th Arkansas Sharpshooter Battalion, for obvious reasons, were no longer able to perform their primary role as skirmishers, and so fell back on their other specialty -- sharpshooting. So, too, with sharpshooters in the fixed works around Atlanta, Petersburg, and other places.
One of my favorite Civil War quotes are the final words of Union General John Sedgwick, killed by a Confederate sharpshooter at Spotsylvania, Virginia. His aide warned him that he was exposing himself too much while positioning his artillery, to which General Sedgwick replied, "They couldn't hit an elephant at this d....."