IIRC, a fair # of credit pulls db, credit board and my fico participants seem to indicate that Amex prefers low util, good income and the fewer inquiries the better, i.e if you spree go with them first. I clearly cannot tell you if you would be approved but I know that when my CC util was near 100% I was in the 660 EX fico range and when I brought both cards down each to < 10 and had overall 3% util My ex went to 750+.
My profile/bucket may be different but I can promise you my approvals would not have gone through at a high util. If possible pay those balances off, as many cards <9 % first and then aim for overall < 9%. I would also suggest making them the only app if possible. I had 740+ fico on EX with 3 recent inq's (6 total) when they approved BCE for $2k. So I imagine if my score was 660+ and high util I would have been denied.
Get that utilization down to at least under 50% prefer < 30%.. That is near maxed out as what is consider maxed is 90% utilization. As you pay it down being utilization your will see a direct correlation of your score increasing by leaps and bounds as well
If you are a current Amex cardholder, feel free to app as all denials will only be a SP