Generally for their credit (vs. charge) cards, you should be at least 700 FICO. That's likely why they tried to pull your other CRs. They do that when an app is borderline. If your tu or EQ are any better, you might let them pull. Otherwise, I'd say while its always possible, it's not likely that you'll get approval on recon. As a rule, Amex only recons when something has changed since the CR. it's possible your explanation of the HPs for a car might make a diff. But your overall FICO is pretty low for an Amex cc.
At least you got delta, so you're in with them. build your history with them and apply again in 6 - 12 mos. if you can pay down your util, it will help with fico and getting approved.