Actually I familiar with the Holland Harness and Ken Nist Suggestions.

You need to read Ken Nist's suggestions again for alternatives.

I want to match 75 Ohm Coax to the theoretical Impedance of the antenna which is 150 Ohms. 150 Homes represents two dipoles (CM4221 in parallel).

How were you planning to connect the two sections together to get 150 ohms? Even if the impedance of each feedpoint is 300 ohms, where they are combined might not be the 150 ohms you expect. The actual combined impedance will depend upon the characteristics of the feedlines that you use to combine them. In particular, the feedline lengths and the conductor spacing, which is the same problem that must be solved with a harness design.

I would simply like to design a 2:1 Balun without using torroids.

Then you have two choices: design a stripline PCB balun for that ratio or use two halfwave coaxial baluns, combine them in parallel for 37.5 ohms and use a 1/4 wave matching section to convert back to 75 ohms.

I also realize now that I simply can not change resistor to 150 OHms as it does not exist. However, I presume that the 75 Ohm resistor does.

No, there is also no 75 ohm resistor, only the 75 ohm impedance of the RG6 coax feedline.

So it seems that I am only lacking the knowledge of what wavelength creates what ratio. For instance you use 1/2 Wavelength with a coax velocity factor of about 0.83 to obtain a 300 Ohm conversion.

The coax for the halfwave coaxial balun must be an electrical halfwave for the required 180 degree phase shift. The VF for foam dielectric is not the same as for solid dielectric. When the current flows into one side of the feedpoint, it must flow out of the other side of the feedpoint.

I can find 1:1 coax baluns which can use a combination of 1/4 Wave and 3/4 or both but I have to date seen no transitions via coax, to transfer the 75 Ohm Coax to 150 Ohm for the antenna.

The way around that problem is to use a different approach.

Each 4-bay section has a nominal feedpoint impedance of 300 ohms. Use a 4:1 coaxial balun for each 4-bay. Combine them in parallel giving you 37.5 ohms. Convert that to 75 ohms with a 1/4 wave matching section of 50 ohm coax.

You will have two problems to solve. You must keep the ends of the coax sealed to prevent the entry of water, and the two 4-bay sections must be connected in phase. You have a 50-50 chance of getting it right. If they are not connected in phase, the main lobe will split in two with a null in the center of aim.

This will give you UHF only. If you want to use the 4228HD for UHF and VHF, you must use toroids. This also has the need to have the two 4-bay sections in phase.