I would expect Second Artillery to be able to react well within seven hours, not seven days, knocking out transport links and fuel depots and reducing the speed of advance to less than 15 km per day.
Providing you know where to send the missiles -- such as your own infrastructure. And how to you get the 15 km per day figure? That's rate of advance in an offensive with active combat -- less than 1 km/hr average. Each vehicles have enough fuel to drive at least 300km without refueling, and divisions carries more fuels and ammo with it than the fuel in the fuel tank, so I don't see how it affects short term rate of advance.
At the beginning stage, the Korean troops have numerical superiority, so instead of fighting through the sporadic resistances, one only need to spare enough troops to pin the opposition and let the follow on echelon to deal with them. This is essentially a deep exploitation of full penetration by an OMG (operational maneuver group) -- except there will be even less resistance, initially.