The entire diameter o the top hat is 14", the radius is 7.5".
Do model it and let's see.
I went back to change the Top Hat dimensions to 7.5" radius and found that I left them 10" like the original ones on the I-10K. You're right, you didn't say they were each 14" long, but that is only 7", so I'll make the radials 7".
That still makes my Top Hat a few inches larger, and when fixed that will help shorten the length and raise the frequency some...assuming this presentation idea is close to corrected.
I'll change the model that I referred to as your modified version and post it up. I could be wrong, but I don't think it will make a huge difference that will get the results up anywhere near 27.732.
Homer, I realize you could disagree with me here, because you were right there during your testing and I'm just assuming, but I based it on these model results. This is the reason I asked you which result you thought were probably best.
BTW, I'm curious, what was your reason for adding the loops, and connecting the Top Hat elements?
Would you agree that might make the hoop look electrically bigger to the antenna?