Look, I literally just went through this process. I got my nuke contract 2 months ago. Not 2 years, not 5 years, or 10 years, or 20 years etc..., but 2 months! I've read posts from a lot of the older guys saying that they signed a contract and shipped out to boot camp practically the next day. That's not how it works anymore. I depped in on April 24, 2012 as an ABH with an original ship date of October 30th, 2012, got my Nuke reclass in July, and now don't ship out until April 15th, 2013. All said and done I'll be in DEP for nearly an entire year before I go to boot. The reason I had to reclass is because I had to wait on some waivers to be approved (age, dependents, and them thinking I was prior service even though I wasn't). Like someone else mentioned, the contract to get into DEP means practically nothing. They don't pay you or give you any types of financial benefits while in DEP, therefore you really don't have an obligation to stick around if you change your mind. By signing a contract you do show the recruiter that your serious about joining, and I believe it makes them more inclined to help you versus someone who says they are just waiting for the right job to open up.
That being said, my advice would be to go back on October 1st (thats when the new fiscal year begins and when a lot more jobs will open up) and let them know your serious about joining as a nuke. If you have to sign on as something else then fine, but be serious with your recruiter and tell him that you do not intend to keep the job that you have and may walk away unless its for nuke. That should get him on the ball to get you reclassed. People do get reclassed all the time nowadays, but just know that its not a guarantee that you will. It will also depend on any waivers you may need and your ability to obtain a security clearance. Your parents being foreigners may unfortunatly hold up the security clearance process for ya.