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Unless you're a stickler for detail install an electronic voltage regulator. They aren't a whole lot more money than a mechanical one, are readily available, and provide more consistent operation.
Can I drive it that way for a little bit, or will I fry the battery?
The fact that you're getting 15V or more proves it. You will fry the battery, ignition, and possibly other items over time. The car should operate at approx 14V, so I wouldn't plan to go very far.