Yes, I believe there are 12-stamp panels for many teams. Probably two for many (if not every) team. I have a panel for Philadelphia Athletics, one for the Red Sox, and two different ones for the Detroit Tigers. I also have a handful of Washington Senators and Chicago White Sox singles. As you noted, these are different from the standard Burke Stamps with facsimile auto.
Here’s my Red Sox Team Stamps Panel:
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http://imageevent.com/derekgranger
HOF "Earliest" Collection (Ideal - Indiv): 244/342 (71.4%)
1914 T330-2 Piedmont Art Stamps......: 114/119 (95.8%)
1923 V100 Willard's Chocolate............: 177/180 (98.3%)