When you write that you've studied loads of scales and arpeggios but "I don't have many jazz heroes to borrow those licks from," it sounds to me like you are facing an obstacle faced by many young musicians today: with all the instructional material and fake books around, it is too easy to think you are learning the music without actually listening to the masters of the music play it. Incidentally, it's not exactly "borrowing the licks" that you want to do - it is learning the language in a different way - like being immersed in a foreign language and foreign culture while learning a language in another country as opposed to sitting in a library and reading books about the language's grammar.
Listen to Louis Armstrong (as another poster suggested), Charlie Parker, Sonny Rollins, Lester Young, Ben Webster, Wes Montgomery, Bill Evans, Miles Davis Quintet, John Coltrane Quartet, Lee Morgan, Chris Potter, Sidney Bechet, Steve Lacy, Herbie Hancock, Ornette Coleman, Tuck Andress, Jim Hall, Lionel Loueke, Billy Holiday, Bobby McFerrin, Lee Morgan ... the list of people worth hearing is huge. but don't listen to 2 minutes of each of them - find one you like and get deeply into their playing - so you notice everything about how they interact with their rhythm sections, know their recordings so well you can sing everything on them, etc... Also go hear live performances as often as you can, and take in what is really happening w/ people playing together, recovering from momentary "mini-crises" so quickly that the audience doesn't notice, etc...
Don't worry - your problem isn't that you will suddenly sound exactly like Sonny Rollins if you listen to him too much - it's that you are trying to play without having spent enough time "listening to how the language is spoken" by the masters. The way to become a great original voice in this music isn't to avoid hearing other people play it, but to build on what you learn from listening.