Bob,
I plan to investigate the 18th edition. It's one of the few I don't have in my collection. Although I am familiar with many of the effects you mention. Especially how the sleeve can steer the elevation pattern. This is the difference between a 3/4 wave ground plane with four 45 degree downward radials and the Vector 4000 design. Just bending the radials upwards rather then down steers the radiation pattern down on the horizon. Adding the loop on top simply widens the bandwidth and reduced the radial length. This upward bending of the radials is something the NEC calculator fails to recognize.
My technique of optimizing the Sigma IV was simple and required since I had to accurately rescale every measurement for FM broadcast. I have a Rohn 45 on the side of my shop. Almost all of my testing is on VHF and two wavelengths above ground. I can reach the antenna from the flat roof on a wood step ladder. Two wavelengths of LMR-400 are connected to the test instrument.
I use a calibrated FIM-71 VHF Field Strength meter to measure the slightest change in gain in the receive mode. The FM broadcast band is great for testing in receive since there are many continuous carries and being FM modulated there is no change in signal as they are modulated. Gain in receive is gain in transmit. I take the care to only tune with V-Pole transmitters rather then CP and only test during midday when conditions are most stable. One translator and another LPFM are about 30 miles away from me and one is using a Dominator close to 98 MHz.
You are absolutely correct about the ridiculous loop diameters required at HF to obtain the 25 degree angle. In fact I can't even do this on the VHF version because the loop ends up being lower then the top of the gamma match and distorts the entire pattern. I do turn the antenna to make sure it truly is maintaining an omni pattern. Because of your noted physical limitations, I have not actually built one at the full 25 degrees.
The best I could do was about 18 degrees before running into the gamma issue. These designs are new for FM and not yet being mass produced as you can see my current antenna is closer to stock angle. I found the biggest jump going from 10 to 15 degrees. Several tenths of a db. Going from 15 to 18degrees showed almost no change on a sensitive instrument. The 15 degree angle is what I have decided on to keep the size practical.
My prototype for testing has every aspect of the antenna adjustable. Radiator length, the length of the four support rods are telescopically adjusted. The loop was an overlapped 3/16 inch copper tube that fit through the holes on the tops of the four elements. By expanding or contracting the overlap on the copper tubing around the elements I could change the loop diameter. Everything would be clamped in place after each adjustment with hose clamps.
I have the prototype fitted with a fixed top ring now that I have the correct measurement. The rest of the prototype is as described and uses no plastic spreaders to support the loop rods so adjustment is easy on VHF. I'll try and dig it out of the shop and take a picture in the next day or two so you can see what it looks like at 15 degrees on VHF.
