From what I understand closed accounts are also considered in account age (this was debated quite a bit on the FICO forums), so closing accounts may not help. With such low utilization and even the number of inquiries, the score drop still seems excessive... so perhaps there might be something else as AsherO said. Do you have any other older account history on your report (going back say at least 5 years)? I could see the impact being more severe to your score if almost your entire report now consists of these new accounts you've opened in a short period of time and you have no older history to balance it out.
Also, I thought AMEX and most other banks will list the specific criteria (what they didn't like in your report -i.e. balances owed too high, too many new accounts, etc. etc.) in the rejection letter, did you not get that information? This should also indirectly tell you what is most negatively impacting your score. Also if you sign up for a credit score service most will tell you the biggest 'negatives' about your report impacting your score as well.