cm: Oh, I don't think, I could list all of these without getting old...
So I guess, the easiest way for you would be to simply go by the pictures and look for ATs, which look just like your AT2214SH, but have a 13 in the model designation - 'cause, unlike the AT13E with its black mounting frame, all the "renames" I'm aware of also have the white mounting frame, just like your 2214 does. And in case you'd happen to find one, that would look right, but doesn't happen to have a 13 in the model designation (like for example an AT84EX), you could always check KAB's pretty good AT overview page (this one:
http://www.kabusa.com/frameset.htm?/at-1.htm) for confirmation, as the listed needle type should be 201-DEM then (= the Pfanstiehl code for the original ATS13), while the listed needle type for the AT14S renames would be 201-DQ instead. Most typically, however, the suffix (like the EX of the AT84EX) should already tell you, whether it's a rename of the AT13E (or rather a rename of the AT14S, like for example the AT85Sa or AT87SL).
But as you've already found out, that you like the sound of the ATS13 in combination with the low inductance generator, too, it wouldn't really seem to matter that much, whether you'd grab an AT13E body (or rename thereof) or an AT14S body (or rename thereof).
Oh, and of course the ATS13 would also fit onto the even older bodies of the AT-VM35 (the predecessor of the AT13E with original needle type VM35-EL) and the AT-VM35F (predecessor of the AT14S with needle type VM35-FD - alias JVC 4MD-20X (with 4DT-20X)) - but iirc, at least the AT-VM35 still sported a slightly different variant of the regular generator version.
Greetings from Munich!
Manfred / lini