If your Z has the double socket neck and 3 ring straphook, it is essentially an S20,
Uh...not exactly. The first series of Zephyrs had these two things starting around 1937, and they have a different bore/bell than a Super 20.
The Zephyrs that are essentially the same as Super 20's in all important construction begin approximately around 280,xxx from all the examples I have seen, but could have started as early as 272,xxx when the Super 20 came out. However, I have seen some Z's up in the higher 270,xxx's that look more like Zephyr Specials (i.e. have that model's slimmer bell--not the fatter one found on the Super 20).
But though the transitions are fuzzier in the first year or so of Super 20 production, when the Z really starts to mirror the Super 20 was when the triangular pant guard was introduced and the cantilevered neck brace was eliminated, again somewhere around 280,xxx. And to me, all the bells on the Z's I have seen from this point on look like Super 20 bells to me.
But of course the OP doesn't care about much of this since his horn comes later. But as you will see the intro was useful because here's the rub--even though the OP's horn will not have the 3-ring hook (but will have the double sleeve neck) it is more like a Super 20 than most of the Z's with the 3-ring hooks, which went away on the Zephyr somewhere around 300,xxx to 305,xxx (ca. 1949 or '50), when the Z was changed to look even more like a S20 with the introduction of sheet metal guards and retiring of the old eyebrow-style guards. And this was pretty much how the Zephyr remained up through the early 70s, and it's basic design pretty much mirrored that the Super 20 until the end.
So when did the Zephyr become an intermediate horn? This is something I've been trying to correct on here for years which was started by Mr. Goodson's line that "after the mid 50s, the Super 20 become an intermediate horn." Well, the key term here is AFTER, and the Z did NOT have its design changed in a major way from ca. 1950 until ca. 1959 or so (around 380,000), when the DS neck was eliminated and the keys changed from brass to nickel-plated. But otherwise, it remained the same horn. Interesting enough, the keys on the Super 20 also became nickel around that time and the DS neck on that one was eliminated as well. But I don't think you'd find many who think the Super 20 became an intermediate model at the start of the 1960s. No, the build quality, weight and just about everything else on King horns remained tank-like and sturdy all the way up through the early Eastlake production.
And I can make these claims since I've owned no less than seven Z tenors (two from the 30s, three from the 40s and two from the 50s). The best one of the bunch was a 1956 tenor (354,xxx) (sold not too long ago) which had all brass keys, the double-socket neck, the triangular pant guard and the Super 20 sheet metal guards. Unlike the earlier Z's that I owned that were more mellow, and in some cases even stuffy, this one had that classic Super 20 King sound, and was a total monster--as much at home for rock as jazz. But it still had that warm, round sound that all my Z's had--a warmth that just can't be found in any new horns that I've played, including the vaunted JK SX90R's which many think to be the logical successor to Kings. Yes, when I A/B'd my '56 Z next to an early ca. 1990 SX90R I bought, though the JK had an equally big sound it was just colder in comparison.
When I relayed this story to my veteran tech with 40 years of experience, he attributed this to the heavy-gauge, cartridge-grade brass that he says they used to make most horns back in the day.
But that sounds like a great Z there, and I betcha you would get a nice Super 20-like Cannonball vibe with it.