The only thing I would add is this. You dont need to drain the radiator. I have an 84 K5 and I replaced the heater core couple years ago. I simply removed the heater hoses and tied them up out of the way. I only lost a shot glass of Coolant. Since you are loosing coolant anyways, there may not be much in the heater core.
Here is another tip. Remove your passenger seat. Youll thank me later. ALso pull back the carpet or get alot of towels rags, etc. I didnt make any mess, but you never know.