Applying early = when?

Hey all... I am currently awaiting a decision from an Early Decision Program that I have applied for. My problem is that acceptances aren't going to be doled out until June. I will have to apply through AADSAS to this school anyways, but would like to save the application costs to other schools if its unneccessary to apply anywhere else (i.e. if I do get accepted on Early Decision). Should I wait until after hearing from the Early Decision Program in June and then, if need be, apply to other schools and risk my application being "late"? ...Or do you think it would be a safer bet to just go ahead and apply to all of my other choice schools as well on May 15, despite the significantly higher application fees associated with applying to several schools? I appreciate your input!

 

I am currently involved in the EDP at University of Minnesota (my state school). I have come across a few others that have early admission as well...i.e. Iowa.