No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
I don't think they'll take your paperwork into account all that much. That's more for mortgages, not auto. I'd wait till the card comes off. There's also next month end though I know March isn't as competitive. Maybe buy now and refi in March with a CU like DCU if your score goes to 675+ EQ?