I could be the head gasket. I drove a newly acquired BMW for months with one of the cylinders leaking from the head gasket. When the leak got bigger, it would overpressurize the system (really hard hoses). The car didn't run bad or overheat, so I didn't realize it was the gasket at first.
Have a compression test or leakdown test done. If that turns out fine, then have the coolant system pressure tested. I would use an old radiator of course. Hopefully a shop can find the problem before you install the new radiator.

Just a quick question: What happens when you run the car without the cap on? Does it build up pressure really fast even though the coolant is still cool?