Detuning a resonant structure is a critical factor to success. Removing the detuning effect of the skirt by a short circuit to ground has a drastic impact on the plot diagram,

     Waller Flag polar plot without detuning  effect

Waller Flag polar plot with the tower properly detuned. This is an actual measure using the program Polar Plot and a sound card. The  source signal is an AM station on 1700 KHz 20 miles south of my QTH. I used to measure it around noon when the signal is only a ground wave vertical signal.