I'm coming around to the conclusion that this actually is a re-badge of the Vivitar Series 1, second edition (or more accurately, of the Tokina lens that became the Vivitar), as Douglas (and others) above suggested.
My evidence:
(1) Specs are very similar -- f/3.5, 70-210mm, 62mm filter thread, approximate 1:4 macro. Admittedly, there are differences too -- ATAN says 13/9 optical configuration, web page below says 14/10.
(2) It looks an awful lot like the second edition Vivitar lens pictured here:
Vivitar 70-210 Series 1 Macro Zooms - Mark Roberts Photography
And I have spent an irrationally long time squinting at that picture. The barrel markings and details (e.g., grip texture) are not exactly the same. But the zoom operates in the same direction (vs. fourth and fifth editions, which appears to go the other way), most of the markings are similarly placed, and the silhouette of the lens looks pretty much identical.
(3) I weighed my lens on my (admittedly cheapo) digital kitchen scale, and it came in at 708g, which is suspiciously close to the 710g figure noted for the Vivitar.
(4) The serial number on my lens is 84000031, which doesn't mean anything by Vivitar's scheme, but it might suggest a build date in 1984, which is in the Series 1 heyday. Plus I bought it on eBay with a Ricoh XR-P camera, also from the 1984-85 timeframe. (I got the 31st one off the assembly line? Did they only make 40?)
(5) Surprisingly enough, this recent eBay auction cemented it for me:
Pentax 35mm 120-600mm ZOOM - F5.6-8 - eBay (item 160266768065 end time Aug-08-08 12:26:17 PDT)
This auction item -- a lens from ACCESS -- is a dead-ringer for the Vivitar 120-600mm.
It has a different brand name (ACCESS vs. my ATAN), but as you'll see in the first picture on that page, it was sold by Magnum Optics in Denver. My lens came with the original manual, and it too came from Magnum Optics. And if you look further, you'll note that the ACCESS lens has a similarly funky serial number (820052) and suggests the same era. (Geez, 52? Did these guys in Colorado just do this as a hobby?)
(6) Further research on the ACCESS brand name turned this up:
Spring 2008 FD Pictures - Photo.net Canon FD Forum
The last poster on that page (Don Boyd, 5/8/08) describes his ACCESS lens manual, and it's the same as my ATAN manual:
President J.K. Wada, check.
Generic picture of some dude operating a lens coating machine, check.
Description of five lenses in the family, check.
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Sooooo, that last bit pretty conclusively indicates that ATAN and ACCESS are the same organization, and the relationship between the 120-600mm ACCESS and the corresponding Vivitar seems pretty clear, so there you have it.
If it's not identical to the Vivitar Series 1, second edition, I'm guessing it's a close relative.
Just documenting this for posterity, and in case anyone's interested.