Since we can only have 5 acceptances per group per week, I think the system should automatically grey any extra available contests on that week so we don't keep applying for them.

I think it does once you are been accepted to 5

Nope. I applied for two shows today after having 5 acceptances that week just to check. I know that on the show app page it tells you that that user cannot be accepted to any more shows that week. Could the system simply cancel applications from people who have already had 5 acceptances as well?

sounds like a good idea