The system is designed for the benefit of the clubs, not players. Tryouts on the same date/time for everyone and if you don't make the team you cant even tryout for a 2nd choice team. That forces parents start talking to coaches/teams well before the tryouts even begin. There is not other way.
Can you imagine the system where you can apply for the job 1 time a year and all the interviews are done on the same day.
Call the AAHA District offices and tell them your grievances. The district sets eval dates not the clubs.
Please tell me how it would work if club A has evals this week and club b has evals next week when club A offers you a contract before club b even has evals. You sign with club A locking you and still go to club b eval, your preferred club and they also offer a contract. You would then have to pay your way out of the 1st contract for your release for club B. The option would also be lose the eval fee for club B or turn down club A in hopes that club B your preferred club takes you. If club B doesn't take you after turning down club A you are again in the hunt for another club.
The best thing to do is eval for your preferred club and if you don't make it start emailing other clubs that may have a need. Years ago my kid got cut and I went on club sites and looked for teams with only 1 goalie and emailed them. I sent out 5 emails and got him 2 after eval tryouts, landing with one of them. The discussion groups every year at every age has post looking for players.