I have a simple suggestion about the league times: *Have the sign-up period as just the sign up period. Delay the start of the actual league games until the sign up period is over. Since most people finish their 4 games before the sign in period ends it makes more sense to delay the games until that time is over.
Except then you have to be available during two time periods, one to sign up, another to play. I'm not sure I understand what you think would be gained by having the periods separate.
