A good letter i think. Im not an expert on anything so im not looking to nit pick or anything else like that but your principal might not or know or understand the differences between argyle jackets or Pc's so mayb a few lines to explain that a PC is usualy black tie etc, other than the the letter seems good and i cant see why you shouldnt get a yes.

That said if they say no im sure we can organise a rabble to crash your dance while you turn up in your tux.

All the best Jordan