Yeah,it sounds like the added pressure of the combustion is getting inside
the cooling system.You say it only takes a few minutes for this rupture to
happen? A symptom of combustion gasses getting into the cooling system is
the overflow tank overflowing.The gasses displace the liquid coolant and
force it into the overflow tank. If you only have a few minutes till
explosion, maybe try emptying the overflow tank and running the engine for
a minute or two.See if  any coolant gets into the overlow tank in this
short amount of time.