What if I used the same common-mode technique for the main vertical element instead of wire? Any magic? Yes and no.
Instead of seeking magic, I just wanted to use a larger element than #18 speaker wire, but most importantly take advantage of the distributed capacitance of the coax to make it less sensitive to its surroundings indoors.
This time, instead of wire, I cut up a bnc jumper for the top element and then when done just barrel the two elements of coax together. (this was done to cut down on waste in case it didn't work - it does, so I could have used a continuous length without the barrel to make up the whole antenna.)
At the base of the jumper, I cut a 1 inch gap in ONLY the braid and trimmed it away making sure that there are no braid frog-hairs still crossing the gap.
I then cut the coax taking velocity factor into account (multiplied the calculated quarter wave by 0.66 for my solid-dielectric coax) and shorted the ends together as measured from the where the shield got cut at the top of the 1-inch gap. Great - that takes care of the inside of the transmission line - but because I'm using outer braid skin depth as the antenna, I had to make up for the shortening by attaching a small pigtail of wire to make it simulate just a plain wire (234 / f Mhz) * 12 = inches.
You'll see this technique used for so-called "double bazookas" on the HF bands where the bandwidth has increased. But I don't really care about bandwidth and want to utilize distributed capacitance.
The other element is the usual 2 - 4 radio shack chokes snapped around the coax a quarter wave down from the bottom cut of the braid at the 1-inch gap feedpoint described above.
Well, what do you know - the bandwidth has increased (usually an indicator of inefficiency, so I'm skeptical at this point). Yawn - I was covered pretty well already without this. I suspect that just the mere change from #18 wire to a larger outer diameter of coax is also helping contribute to the broadening.
But the goal of reducing the interaction with surrounding elements has improved! I have a very very weak ATIS station that I could knock out just by getting my hand near the former antenna with bare wire. Now, the station is just as weak, but I can place my hand anywhere on the coax and not make it drop out. Seems to be working!
The other good point is that this version seems to have the same vertical lobes just like my bare-wire whip version. I don't like surprises either good or bad.
This is a very long way to go just to reverse-feed a piece of coax to make it emulate a bare wire! (This is exactly how my "shielded coax loops" for HF work. The main advantage is the distributed capacitance for balance, not any sort of shielding, and that's what got me thinking about the vertical.....)
Where this thing is hanging is pretty free from obstacles, so I'm going to revert back to the wire. Performance is similar.
What it did do is give me an option for window mounting which happens to be an aluminum frame. This way I can try and reduce the coupling to the frame. I might even get brave enough to try the half-square broadside array made out mostly coax like this. Maybe next month!