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I have nothing to offer the original poster except a brief addendum on the theory of operation. As mentioned above, the spoke radials’ radiation cancels if they are physically mated at 180 degrees. The principal of operation is that the hat changes the current distribution in the vertical radiator.
That helps because it is the current which produces radiation (accelerating electrons). Essentially, the more accelerating electrons in a conductor the more radiation. In a vertical monopole the current at the top of the antenna has to be zero since the electrons have nowhere to go beyond the tip. The current at the top of the radiator is zero and that near the top is small. The capacitive hat gives the electrons somewhere to go and thus raises the current at and near the top of the radiator in effect “pulling up” the current distribution along the whole radiator. This increase in current due to redistribution affects increased radiation.
I have not used hats on AM but for FM I have measured remarkable increases in radiation with a hat. One was simply a soda can placed over the tip of a short whip and another was a spoke type hat fashioned with a few inches of solid copper wire. I didn’t pursue this beyond a simple experiment but the increase in radiation could have been due to tuning effects as well as current redistribution.