1) 5 inquiries in the past 12 months may not sound like a lot to you, but it very well may sound like a lot to Cap1, and, unfortunately, its Cap1 who matters.
2) The scores you're seeing from AmEx Secure are not FICO scores; they're FAKO. There could very well be a sizeable discrepancy between the two.
3) You sending them AmEx Secure reports, i.e. not directly from the CRAs, are not likely going to change anyone's mind, especially in view of the above two points.