While I know NYU is more flexible with waiving out of ED than other schools, do know that they meet 100% of need.
So you should be ok.
Saying another school is cheaper is not relevant. You applied ED full well knowing you are bound if you get in, short of it not being affordable.
That it is more expensive does not make it unaffordable.
You should not have applied ED. You gamed the system and now you have a pickle.
You should live up to your commitment, assuming it’s affordable (which doesn’t mean less expensive).
Good luck.