I figured it out the issue with the gift card purchase page, Delta uses a third-party credit card verification service that serves up a pop-up in my browser (FIrefox with pop-ups disabled).
Purchase works on a different browser with pop-ups allowed. Same issue occurs on Delta.com when trying to add a new credit card for regular purchases.

The "card rejected" message happened immediately, which also shows rejection happens at the website, not at my credit card issuer. I blame Delta's web design team more than my browser, which Is doing exactly what I want.