Check out the musicianship courses over at www.dickgrove.com. I think they will be perfect for you. Your experience will help a lot, but these courses will absolutely bridge the gap for you, to where all your questions will start to fall away, as you begin to hear the way you need to in order to play jazz.
I myself was a student, so I know firsthand how good his courses are. I have a bookshelf full of @ a hundred books and resources, but have never come across any materials that explain the information you need in a way that works like his courses.
Jazz musicians can play jazz like they can breathe, or walk. They are hearing or humming music while they walk down the street, take a shower, driving in the car. The key to improvising is how well your ear is developed, nothing more.
Point is, in order to play jazz for real, it has to come easy, almost automatically. And in order to get to the point where it's easy, you have to work really hard to develop your ear to higher levels than ever before. But once you do, there's no more wondering how to play or understand. At that point, you will wonder how it is possible NOT to play or understand jazz! : )
Think of it like language, because that is exactly what it is. A person may familiarize themselves with a new language, to the point that they are comfortable with it, they recognize it. But that doesn't mean they can speak it on their own yet, or use it spontaneously. But in your native language, you could literally get up in public if you had to, and just start talking about any subject you know something about. No preparation, etc. That's where we need to get to with music in order to play jazz.
Also, check out the cd This Meets That by the great guitarist John Scofield. You will love it.