I think rugby would be great. You could choose to be one position;
Scrum half, Fly half, inside centre, outside centre, winger, flanker, 2nd row, number 8, full back. Though being hooker or tighthead/loose head prop would be pretty dull.
Stats could be like NSS3, except adding Drop Kicks, Long Kicks, Speed of Kicks, Pass Length, etc.
The team should definately look into it.