Chase Freedom was the first unsecured card I applied for in my rebuild. My 3 scores were something like 612, 625, and 645. I had my secured cards at least 7 months(I don't remember the exact length for each of them). I had a tax lien, a chargeoff that was about to fall off in a few months, and some 30 day lates on an otherwise paid as agreed car loan(the lates were more than 2 years old). I used the prequalifier link for chase found here:
http://ficoforums.myfico.com/t5/Credit-Cards/Pre-Approval-Sites-June-2015/m-p/4059266
and it said prequalified for Freedom and Slate, so I rolled the dice. The Chase prequalified offers are said to be pretty reliable, but no prequalified offer is guaranteed. Getting approved for the Freedom made me take a gamble on Discover. While they have a pre-qualifier link there, a lot of people have a low opinion of how reliable it is. But I figured if Chase would approve me with a 4500 line, I might have a decent chance at a Discover. I got it, but by the skin of my teeth going by the small credit limit they gave me and the two hard pulls. Chase gave me a decent CL, but also 2 hard pulls.
As always, YMMV. At some point, you're just going to have to roll the dice and give it a shot if you want an unsecured card, because no matter what your score is or how solid a pre-approval looks, there is always a chance of denial. Your scores are in a similar range that mine were, so it could either way, you're in that border zone. Your EX might get you an AMEX offer, check their prequal as well maybe.
Or just wait a few more months, get a bit more juice from your efforts. Doesn't hurt to wait.
EDIT - Just looked up what exactly my scores were when I apped, 632, 634, & 641.
