I don't think the ASW is going to help get good financialaid nor do I think it will harm your chances. If you can go though it might inform you about the school which could help you make your choice.
Congratulations! I think if at all possible you should definitely visit both schools. Have you received any financialaid information yet? That will also be a big factor.
... score won't change your financialaid outcome. Since you're an ... a top school. HYS's financialaid is also pure need-based ... you should see some decent financialaid based on your background if ...