Finally got approved for a Discover Card! Hooray 
Process was a bit weird, though: The "prequalification" page is a joke, but I took a chance and applied anyways. They counteroffered with another unsecured Discover Card so I took it. Thing is, with that generic offer I had no idea which card the original application was pointing toward. Maybe it was a lower rate or a different cashback structure?
Anyhow, it wasn't a rejection so I'm pleased because I have been wanting to get a Discover card for a few years now. 