The timing is horribly bad when it sounds like you have gotten your act together, but I wouldn't worry too much about it. You should just reapply in 2-3 months when your new 'debt' situation is reflected on your credit report. If you just paid them off, then it isn't going to show yet.
Awesome job at getting your slate wiped clean. If Amex doesn't want you back, then screw em. Plenty of other cards in the sea.
I remember when I was younger (23, I think), and Discover card turned me down, despite perfect credit and responsible credit card use (I had a credit card since I was 18). Never forgave them (not that I'd want that crappy card anyway, now).