Bob, I agree one of the images you posted is similar to the vertical side of the Saturn, being very much like the Sigma2.
I agree there would probably be another small circular slug inside the insulator that is connected to the small wire inside, and if that small wire has a coil, then the slug would likely be positioned between that coil and the SO239---acting as a feeder connection point for the horizontal feeder rods, which I believe are likely fed directly by the coax with no matching device. The matching coil would be above this connection point and would feed the vertical side of the antenna. I think we more or less agree on how the construction might look inside the insulator on the Saturn.
I also think this antenna uses three independent diamond shaped quad elements with the 1/2 wave peripheral wires (sides 2 & 3) serving as the horizontal polarity radiators. I also see the 1/2 wave wires supported in the middle by the grounded separator arms which for me creates a setup similar to the configuration of a radiating grounded yagi element. As I note above, I see this horizontal quad element being direct fed with two possibilities for the feeding mechanism for this bugger.
Originally, I thought in my minds eye this was a form of a folded 1/2 wave dipole positioned as the leading edge (1st side) of each quad element, feeding the 1/2 wave perimeter wire (sides 2 & 3) as noted above. I don't know for sure, but I think a true folded dipole will exhibit about 300 ohms of resistance at the feed point. For me, this one looked like half of a folded dipole, so I was thinking it may show a feed point impedance of about 150 ohms. With three such systems connected in parallel, I would expect the net impedance at such a feed point connection to likely be 50 ohms---and therefore need no matching device. I was reminded of the folded GP image below when I first saw the Saturn manual:
The second idea I had was maybe this antenna is similar to the matching at the bottom of the AstroPlane. But, instead of end feeding the 1/4 wave top element at a current node on the grounded hub of the AP, this one is instead end feeding a 1/2 wave radiating element from a voltage node at both the ends of the balun wire making up part of the 1/2 folded dipole. Again, with these three quads connected in parallel---the net feed point impedance should be about 50 ohms. I also think theory suggest that folded dipoles provide very nice bandwidth, and this would be a plus. I'm not too sure that the AstroPlane does not use some of this idea in its feeding scheme. In the patent Avanti does describe the bottom as some form of a open or closed ended cubical circuit I think.
Bob, I'm just piddlin' with my imagination, and not real sure about any of this however.
You and I just recently had a discussion regarding the use of 1/2 wl, 1/4 wl, or random length feed lines, and here again we have Avanti talking about such things in the Saturn manual. I also recently read, what looks like a new article on vertical monopoles by W8JI, where he again talks about the affects on performance etc., with different length feed lines and heights above ground that result in worst case scenarios. So, I'm still not sure what all this business is about with feed line length. Your claim that it is all CB BS may be the case, but these words I keep reading by such dignitaries leaves me to wonder. Avanti recommends again the use of 1/2 wavelength or multiples for the feed line on the Satrun. Avanti claims that it helps improve the polarity separation for the antenna, or as you note "...it keeps the phase separation at the switch box." For years I had heard not to use a resonant feed line like a 1/2 wavelength or multiples, because it encouraged CMC to flow into a low impedance condition more easily. I'm sure the Avanti engineers tested their ideas, both in theory, and in the real world, so I'm still wondering.
I don't know anything really about the cloverleaf designed antenna, but that it has a low angle of radiation horizontally, and is broad banded enough for some multiband use. I have seen them with stub matching and using folded dipoles to feed a modified quad element, as I note above.
What I think Avanti is good at, with these antennas, is using the mysteries of the circuit to build antennas that follow the principals of the circuit to produce the same results in many different configurations, as in the case of the Saturn horizontal side and the AstroPlane. I think in their Sigma IV design Avanti used such skills to make that really long radiator work as you have experienced, in a rather non-apparent collinear manner---even while other's say "...such a long radiator is nothing more than a cloud warmer."
This antenna must be a monster, but I would love to build and test that thing.