While the 30-30 is my favorite for running shots, at those ranges, I'd prefer a 308, so, i'd go with a light fast handling rifle, like the 88 Winchester, or BLR and though I hate to have to use a scope, I'd use one under those conditions, probably a 4X, or a variable in that range.
Practice, is key, and fast target aquisition is a big part of that. Some ranges have running deer set ups, use 'em.
Try setting your rifle on the bench, turn away. Turn back, pick up and fire as quickly as possible.
Try the rolling a tire down a hill stunt, if you can find a slave willing to roll the tires up the hill for you.
Practice, and the shot is not difficult.