Congratulations on your decision to go into the Army. It's where I got my start, and I'm glad I did.
Your parents won't hang on to that until you get done with Basic and AIT? It's not like it'll take a lot of room, and, if they're going to hold your own room for when you visit, what skin is it off their nose to have it in there all neatly boxed up? Since the chances are that you'll get a state-side assignment, first, (unless you volunteered for Korea) I'd ask them to hold it for you. Once you get your reporting orders, you'll be able to take it with you and finish it. You could even chance having it shipped overseas if you get stationed in Germany or Korea, but I wouldn't recommend that.
If you put as much time as you imply into this, then just getting rid of it is a waste.