I've learnt this about costume parties: go all out. Really try to be the thing you're aiming for, and you get two results.
(1) People appreciate the effort you've put in and you're making their day. Seriously, you suddenly "appear" on their radar and you get spontaneous well wishes "that's amazing", "great costume mate" etc. That makes you feel good, in turn, and that's a great thing to hold on to.
(2) You make it harder for an NT trying to size you up with their "normal" hidden rules because now your appearance is governed by the character you came as, and not your usual dressing code - and guess what? You've dulled some of their instincts. They've got to talk to you now and listen to you! That evens the playing field I think, and you can let your costume "carry you" through the initial social awkwardness. This does wonders for your confidence with groups, which they pick up on straight away, and some of this confidence may even rub off on you when the costume is no longer there...