^^^^ Im surprised that no one has said the cap yet until now.... That would be my first suspect if pressure is extremely high being as how the cap is what controls the pressure.....
I'd even more suspect the cap being that it seems as though there is a lot of old equipment and also the fact that the radiator hose leak started after the car was shut down for a few minutes....
If the head gasket was leaking, the pressure would drop pretty quick once the car was turned off but insted cause of leaking back into the cylinder, but insted it increased which is normal (so to speak).. Here is why, when you shut a car off, for the first 5 minutes or so of no coolant flow, the coolant temp increases in the engine. As most know, as it heats up, it expands well if there is no room for expansion to accure, then it increases pressure.. The cap regulates pressure by bleeding off the pressure and created form the expansion to the coolant overflow bottle.... If the cap cant relieve the pressure, then something has to give, thus leaks form..