From your description of the problem, I'm guessing you have a fancy split Flying Quail or Moto-Meter radiator cap. These caps are attractive, but are notorious for allowing hot coolant to surge out under power demands, such as you describe. I'm also guessing your radiator doesn't have the all-important baffle in the upper tank. Without that baffle to re-direct boiling water back down through the radiator, the coolant follows the path of least resistance and heads for the radiator filler neck. The result is a messy overflow onto your hood and windshield. You know all about THAT, don't you?!?
Yes, one way to help curb this problem is to keep the coolant level a little lower than usual, yet not enough to compromise cooling efficiency. Do not fill the radiator to just below the filler neck. That's too much coolant. The level should be just above the top of the core inside the top tank, which is considerably lower than if the top tank were filled. As the water heats up, it expands and will exit wherever it can. Too much water/coolant exacerbates the problem. Once the water starts flowing out of the radiator filler neck, people often think the engine is overheating. Well, it WILL overheat if enough coolant is lost. What happens when the coolant in the radiator heats up and begins flowing out of the split radiator cap, is it becomes a self-perpetuating puking action that will only cease when the car is stopped for a while or if you can coast downhill for quite a distance. Try putting on a regular factory-style flat cap in place of your fancy two-piece radiator cap and see if the problem persists with water rushing out of the overfill tube. If it does, then there are other issues to contend with, such as a weak radiator core (especially if it is only a two-tube core sold by J.C. Whitney) or a blown head gasket, as has already been suggested. I should think if the head gasket were blown, however, you'd notice a drop in performance and perhaps misfiring. Any of that going on with your car?
Marshall