Wow, having read your post and also some of your responses to comments, I've gotta say, you can come off a bit as quite the entitled asshole. I say that in the hope thag you come to realize how much of a non issue this is.

That said, I've gone abroad for school and had a similar thing with my parents in terms of packing up early, and I agree pretty much completely with what strafey said. Just pack up the stuff you're not using every day, so when you are getting nagged, you can point to tangible progress that you have made, and can easily explain that you're capable of taking care of the rest, in a timely manner, later on.

Other than that, they're your parents. Whether they're paying for your schooling or not, they still took care of you up until this point. At the very least I'd say pick your battles; this is not the one you need to stand your ground on, especially as you're already concerned about your worsening relationship with them right before you leave.