Is there any way to cancel out of a contest once you have been accepted? As an example I applied for the APA contest, but if I advance to the next round, I have to be able to cancel events I've already been accepted to in order to compete in the next round.

There isn't a way. Perhaps you can ask Alex to remove you from the event. He may say no though. Be more careful next time.

tbonepower, I think i could help you on your issue with the APA competitions. Check your messages and reply. =)