Well this sounds like to me that you may have a bad thermostat(located between top radiator hose and motor block).
The thermostat is not operating properly(not opening when reaching temp) causing pressure build-up in the antifreeze lines(hoses).
Now since you by-passed the heater core will even cause more pressure because the heater core allows the antifreeze to flow more freely through the system, this will make the car overheat easier.
I would recomend a leak-down test through the radiator(radiator pressure test) and check for antifreeze and air leakage(spray bottle with soapy water around head gasket area).
It is possible that you may have a head gasket leak(doesnt always leak into the oil part) but you did not say if radiator was going low on antifreeze after running awhile(could be leaking out the exhaust(white smoke out exhaust) or even leaking out on the side of motor).