I have an industrial technique for removing calcification/oxidisation/corrosion but it will do the trick. Go to your local supermarket and search for "citric acid powder" in the baking aisle. Buy 2 of the small shaker things full of this stuff, dissolve it in a bucket of warm water then dump it into the radiator and drive for a day (normal day to day driving should be enough). Make sure you run it with the heaters on full so it circulates through the heater core and then drain everything out of the cooling system - and flush it like your life depends on it. You may feel a little unwell when you see what comes out of the radiator. Be warned - if there are any breaches in the cooling system anywhere that have been plugged up with crud, the citric acid bath will eat through the garbage. This stuff will also dissolve rust so there might be a chance that any large flakes in the block that have been oxidising quietly in there will make a guest appearance. I've used citric acid bathing to remove rust and power flush a heater core and it works really well.