wow impressive! i wrote a hasty PS in december trying to get in by the priority deadline of my school so i could be considered for scholarships... was to engulfed in studying! if i dont get in i'll be taking full advantage of this for next year!
You should be fine for HYS. Typically people recommend applying early for primarily scholarships as there is a larger pool of $$$ in the fall. But in the case of HYS, they only do financial aid so you applying in January will be fine. Good luck!