Op, I apologize that there has not been any replies to this yet. From what I am seeing, you have made strides in getting your credit scores up and strengthening your profile. You have some $$ to work with as well, so overall you appear to have a nice foundation to work off of.
Any specific reason as to why you want the Jet Blue card in particular, other than the obvious? While ymmv, I have seen more or less that to get the Jet Blue card, the average score needed would be around 700. Then, 750 for the Jet Blue Plus. Now this is just reading up on articles with what they believe the average scores needed were. With your current scores, maybe the Jet Blue is more in range??
On refinancing the vehicle, if you can find a rate that makes sense for you financially then maybe it is worth it.
Getting a third card would be good for you, whether it is Jet Blue or something else. But for any app, I would suggest that you do searches on different lenders in the forums here, like Barclays for instance, and read up on how they are for people with past BK's. Also, search for approvals of specific cards to get some of the data points of what each profile looked like. Gain as much helpful info in your favor ahead of time.