I am a classically trained pianist, and I consider myself to be decent at playing. However I'm a poor sight in jazz, which is something that I really like. This summer I plan to study jazz thoroughly, so that by the end of my holidays I can play some decent solos, comp adequately, and even interpret some jazz standards and play my own versions.
I understand that there are two paths to take when learning jazz: transcribing the greats, and learning theory. I also know that jazz education was not readily available during much of the 20th century, and that's why many people learned by transcribing.
I have come across websites and blogs that promote ear-training and transcribing over learning music theory such as this and this (even the jazz theory books that I own emphasize the importance of transcribing). They say that transcribing allows you to eventually be able to "hear your solos in your head" before playing them, as well as allowing you to mimic others and eventually develop your own style. I want to acquire both these skills.
Similarly music theory can also improve improvisational skills, but it doesn't teach melodic innovation. That is, I may have a very good idea of what notes will "sound good" but I won't know be able to think of any innovative melody. This is why I believe that transcription will be more important for me than theory.
But at the same time, I think that theory can really help with comping and playing harmony.
So to sum up: Are there any things that music theory can do which transcription can't do? If so, how much importance should I give to learning jazz theory, that is, approximately how much time should I take from transcription and allocate to theory?
Thank you for your answers, and feel free to correct me if I've said anything wrong.
PS. I own both the Jazz Theory Book and the Jazz Piano Book (both by Mark Levine). I plan to exhaust the information in them eventually, if not now.