I work for Horizon NJ Health (another Family Care HMO, the best by the way!!). It is a violation of federal regulation for a provider to bill you and/or balance-bill you for covered services. So this whole thing about you paying x-dollars a month, FORGET IT.
#2 - contact Americhoice's member services and ask to file a formal complaint. This is, unfortunately, the fastest way to get this taken care of. State that you are on Plan C which covers orthodontics (off the top of my head I think that's right too) and a participating provider (he is par, right?) is telling you a covered service has to be paid for out of pocket, pretty much exactly what you've written.
#3 - if that doesn't work, insist that the dentist's office contact their provider representative for clarification. Also, I'm pretty sure it's the dentist's responsibility to obtain the preauth, not yours. I know HNJH members don't have to get their own auths.