Y'know Nate, it looked to me like it could've been done the way you described but I did it the hard way. Besides, my cooling system needed flushing and freshening up anyway. It was a PITA and refilling the cooling system is really fun (all that air "burping" and the possible attendant overheating if you're not careful). Some guy named Walter C. Avrea designed it, and he should be:
Kurt