It would still be Jasper Shells (like the SSB and the 6ply RB drums). I'm not all that up on edge profiles but as far as I can tell (I own sets with all the badges) they didn't change any major construction details when they changed badges, they just changed badges. Of course production methods did evolve through the years but Gretsch seemed to try to stay true to their successful "recipe" as much as possible. Generally speaking the Square badge drums were built to a higher degree of quality control as the marketplace pretty well demanded that starting in the mid 80's forward (customers got fussier about fit and finish). The hardware was much better once they switched over to the Tech-ware stuff which was right around the introduction of the new badge. The hardware (hoops, lugs) was still American made, which actually means the chrome-plating wasn't the greatest (the imported parts they use today have much better plating than the stuff they used in the 70's and 80's).
The different badge designs do help to differentiate the different eras of construction, but they don't, at least in my experience, correlate to any major design changes in the way the drums were constructed. Changes were made as things evolved but those changes were gradual and not directly tied to the changes in badge design.