There are so many reasonable solutions to this, its hard to understand why change has not occurred yet. And many of these solutions involve the club/tournament (they are the same people) owners making more money.
"Travel" sports isn't what it used to be. In years past, the best kid in town (in whatever sport it was) played for some select team somewhere. That was it. Now, a TON of kids play "travel". I am not trying to disparage these kids. Its great that they are playing, and it beats xbox. But travel sports have now grown well beyond just the kids that will get college scholarships and/or go pro. An example of all of this is the fact that some kids are on travel lacrosse teams that would get smoked by their own town team - because the top kids on their town team (and other town teams) are playing for higher level travel teams.
Focusing on lacrosse - in northern climates, the town season is very short. Travel lets these kids play another 6-8 weeks or so, and the kids love the tournaments. Owners should capitalize on this growing market and gear their programing to these kids. You can still have it be grade based at the AAA (or elite, or AA, or whatever name you want to give), and make this level relatively shallow to ensure that only the top players get in and that it will be competitive for these kids. But for everyone else (and this includes the many teams that market themselves as AA or elite but really aren't) age based is much better. And it can be either calendar year of Sept-Aug, I don't care and I don't think it makes a difference.
The bottom line is that there is no more growth in the area of elite players. Every single elite player is already playing club lacrosse. But there is still more room for growth amongst every other level of player. June and July provide very little competition in terms of kids sports and activities. If the club owners were smart, they would be presiding over clubs and tournaments with all of the following teams - AAA (can still do it by grade), AA, A, B. But mediocre or newer players can not compete against older kids from some far away state, so it hasn't really gotten off the ground on the lower ends. But if you make sure that everyone is within a 12 mos. birth window, you can have competitive fun lacrosse amongst teams from all over the country at all kinds of levels of skill and athleticism.
And for the "sorry your kid got cut crowd", my kids have all made very good teams and played well. But I have seen too many people be one and done with a club due to holdbacks, and say things like "why should I spend money and do all of this travel to watch my kid play against 14 year olds when he is only 12".