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Discover doesn't recon.. What the computer says is the result.
Something has to be holding your EQ score down.. You say you don't have any baddies being lates or CO's or CA's? Is your utilization really high? As you stated no baddies form your original post, your utilization has to be high or that and a ton of inquiries as 647 is pretty low for nothing bad on a credit profile. Please don't take that personally.
Discover is a very very weird lender. They will approve someone just out of BK7 and decline people in the 700's.. No one can really say for sure whom or who not they will approve. I have seen people in the 640 range as yourself get approved. All depends on your whole credit picture. More info would be helpful as why is your score 640ish, what is your AAoA, other Credit cards if so what, inquiries, etc.
3 weeks isn't very long. I know we all get excited about score jumps, but it's not just about score, it's about the whole profile.
I would wait 3-6 months before reapplying as typically your profile will not have changed significantly enough in 3 weeks to warrant a different decision. As stated they don't really recon so what you get is what you get. I wouldn't waste another HP at this point.
I would wait a month personally.. Wait for your new card to show up as optimal scoring for Fico's is 2/3 CC showing on report and make sure your one card has less < 30% utilization and only one card showing a balance upon applying. Make sure you check your reports prior more so Equifax that you are indeed < 30% of your credit line showing at the time before choose to apply for Discover or any card for that matter for best results. Best of luck and hope this helps a bit.