In my JLPT practice book, there is a question that asks you to put words in the correct order:
朝の満員電車の中で、大きな音で
____ ____ ____ ____若者がいる。
What I put down was:
朝の満員電車の中で、大きな音で 迷惑きわまりない音楽を聞いている 若者がいる。
But the correct answer is:
朝の満員電車の中で、大きな音で 音楽を聞いている迷惑きわまりない 若者がいる。
From what I can tell, it seems that the first sentence is saying that it is the music that is annoying, and the second sentence is that the kids are annoying, but I do not see why one is any more grammatically correct than the other.
It's not completely clear from your question whether the problem asks for "any grammatical order" or "the most natural order". While your answer is grammatically correct, the "correct answer" is more natural, and I'll try to explain why.
While "annoying" is one translation of 迷惑, often a more fitting translation is "inconsiderate". Although I have seen the word used in constructs like 迷惑な天気 where no one is really to blame, I would say that much more frequently it is used in cases where there is actually someone who is being considered "inconsiderate". Even when used in constructs like 迷惑な音楽, the speaker will tend to have somebody in mind who is being "inconsiderate" by playing the music.
In this case, the "inconsiderate" culprit is obvious, it's the kid(s) listening to music in the packed train. Therefore, it seems more natural to let 迷惑きわまりない describe the kid(s).
