CLR does horrible things to aluminum...... don't really recommend that. Just give it a try with straight water first.
coolant (heatant?) flows from the hose at the intake manifold, thru the core, and then back into the water pump via the hose to the steel pipe that plugs in to it by the power steering pump. Flush in the REVERSE direction first, and then the other way. Go both directions a couple times, ending in the reverse direction. Then, put the hoses back on, trying to lose as little coolant as possible. Run the engine, burp the system, and see how it feels.