Lacrosse and Soccer work as long as you don't play in every off season fall pick up tournament, we have done it.
On the best rounded athlete, just look at college football kids going D1, a large number of them are listed as Athletes under position. That kind of says it all. A great athlete will always find a team and a position.
The Canadians and Iroquois are the best lax players. Tell that to the lax/soccer player or lax/basketball player.