Here is an idea for another yagi design that provides for a balanced radiator that is direct fed and isolated from the boom. It requires no matching device. The model shows that a choke may not be necessary for CMC, unless the issue develops.
Below is a link to the Website with this design, including some Eznec modeling performance details and some pictures. Unfortunately there were are no dimensions, so I had to do a lot of guessing. But, I took my time trying to figure it all out and I think I got close tweaking this idea. The effect is in the angle of the driven element ends towards the reflector.
I ended up with a bit longer boom at 16' feet and my performance data is a little different, but it is close. This model is at 59' feet high, at 27.205 MHz instead of 27.555 MHz...which Henry use for his model. Some should recognize the author of this link.
http://www.hpsd.nl/f-yagi/4el-f-yagi
Below is my model which includes a mast which is not included in the linked model. The driven element is isolated (ISO) 2" inches above the boom and the other elements are supported by the boom. I can't tell for sure, but I think Henry's model has all the elements in the same plane and that may make the difference between our models. The feed point is noted by a faint (O) in the middle of the driven element.
Abbreviations in the title:
CDF = the antenna uses a direct fee in the center of the isolated driven element.
wISO = the driven element is isolation from the boom.
nC = model shows no choke necessary due to very low currents on the mast.