There was a legal method... but I believe they needed the AZ SoS to pull it off. Hawaii didn't have to cooperate, but AZ didn't have to put BHO on the ballot if they didn't. Request had to be related to official business (verifying eligibility would, but has to come from SoS)
I agree that the BC is a moot point- it comes down to is he a natural-born citizen, but no court wants to hear the argument as to how exactly that's defined.