Brilliant idea ... definitely a missing point. Funnily enough i was looking into this myself but I'd be proud of you if you could do it!
My thoughts are a game along the lines of cricket. Two main ways to go. Either two set plays in action (one for each team) with opposite numbers attacking each other, the ref, sideline judges and video replay with the ball could make for an auto win? Alternately everyone in their starting positions (like Knights) but with linkages between say the opposite numbers or in groups (ie backs, flank, forward, etc). One final idea is there a bunch of silly rules (like cricket) and maybe they could be called into play (like forward pass (oops that's rugby), umm offside (no that's soccor, umm well you probably know NFL better than me!).
Anyway, post some visuals for us (even if you draw it on a piece of paper and add a link to it through the likes of photobook etc).
Have fun, can't wait.