Firstly, don't be sorry. This isn't your fault it would be Apple's.
Secondly, you said you managed to get on the phone with someone the first time. I think you need to try and get into contact with someone and explain the situation, because it seems that Apple really doesn't know what they want. It seems really unfair that you guys got rejected twice, for contradicting reasons, and letting apps like Order and Chaos on the store no problem. Once they realize they have contradicted themselves, they are going to have to make some decision as to what to do.
Thirdly, what the heck are you gonna do if they insist you return to the original method? Would you have to completely rework the game again?
Anyway, I can understand that you guys must be having an awful time wiith this, and you guys are desperate to get the game on the store as much as we are desperate to play it, but there is light at the end of the tunnel.
I'm going to be really curious as to how Apple responds when they realize they messed up.