If I were you I would apply for Chase biz SW first, then Chase personal SW, then Amex Hilton Aspire.

Chase biz cards are not counted towards 5/24. In my experience, as long as you have a good history with Amex, they are likely to approve your application to their premium credit cards.

As for the 4 or 5 Amex card rules, if it really is an issue for you, when you call recon you can ask to close one of your Amex credit cards. IIRC some people can get 6 Amex credit cards (plus charge cards), so the 4 or 5 is not a hard rule for everyone.