tarokun wrote:Bueller_007, your translation and analysis make the most sense.
Wish Peter and his JPod101 crew could give a definitive response here.
あなたの夢を見る means "to dream of you", but I think it's unlikely that the singer would drop the を and change it into あなたの夢見る[ほど], which, if you assume it is grammatically correct (and why wouldn't you), carries quite a different meaning. Because dropping the particle leads to ambuguity, it's likely that it would stay in.
I guess it's possible that the を particle was dropped to fit the rhythm of the song, but if this were the case, the singer could just as easily have said あなた
を夢見るほど強く, which would have kept the "to dream of you" meaning, has the same rhythm, and would have kept things clear.
We don't really have any reason to think that the を particle was dropped, so personally, I'm inclined to choose the translation that assumes grammatical correctness in the Japanese version:
"I love you as much as you [could ever] dream." I wouldn't even have thought of translating it otherwise until I saw the English version that was posted on that website.