For me AMEX has always been sketchy. In the past I had applied for a Plat card with them online and was instantly denied. I called up the next day and applied over the phone and was instantly approved.
More recently I applied for a Costco Amex card. Been with AMEX since 2000, I've had a plat card with them in the past which I downgraded to a gold card, never been late with anything, FICO's 760+, income $250K +, and I was denied.
Since Amex has their own little internal scoring system I think it's difficult to say. My experience has been it's a total crap shoot.
P.S. Amex is one of the companies I'm moving away from as they seem so **bleep** inconsistent with their policies. Customer service has also been spotty for me lately.
Any prior AMEX experience, or current holder of another AMEX card? Your income is fine and FICO is good, but prior lates could be problematic with AMEX. I got a Starwood card about 4 years ago, instant approval online for a large CL, but I was already a Gold Card holder for 25 years before that so that greased the skids. I'd say you have 50/50 chance of getting approved.