Cooling System problems

[1973Mach1]

I recently bought a 1973 Ford Mustang Mach I, with a rebuilt 351 Cleveland. There several strange occurrences within the cooling system, most likely all related in someway.
First, when the engine starts to get warm, and you step on the gas, the top radiator hose collapses completely. Next, when we attempt to run the engine without the radiator cap (as all the manuals say is
possible), the coolant first goes down and appears to be circulating, but then it will quickly rise up and begin to overflow. Most
mysterious of all, when the coolant is overflowing, if the engine is shut off, the coolant is forced out of the radiator so quickly that it gushes a stream the diameter of the cap at least a foot out of the radiator. (Also, the engine never overheats when it does these things, the gauge reads in the bottom quarter or less, and the thermostat does open)
In order to correct these problems, I have tried at least five different thermostat, of both the low temp. and the high temp., as well as even drilling a small hole in the thermostat like the older ones
used to. Also, we tried replacing the radiator, the hoses and even the cap, and still the problem persists. Lastly, I removed the water pump and it appeared normal, spun cleanly, and showed no signs of corrosion.
Any help you could give us as to why all of these problems occur would be appreciated.