Illinois could just have easily accused you of the same thing.
When nationals was at the University of Illinois at Urbana-Champaign in 2005, Illinois Science Olympiad was one of the sponsors, and its logo back then was exactly the same as you showed in designs 2 and 3.
Sorry to break it to you, but the periodic table T-shirt design is extremely common. Just look at last year's national T-shirt design. (You should feel lucky, however, that you can spell out "Franklin" without omitting any letters. Many other schools can't.)
Ames Science Olympiad (Iowa)
2009 ASU: Team C51
2008 GWU: Cell Biology, 9th
2006 IU: Balloon Race, 6th; Compute This, 3rd; Disease Detectives, 3rd
2005 UIUC: Robo-Billiards, 3rd; Compute This, 7th