You seem to already know the notes and intervals, so my suggestion is to listen to the different styles of playing for getting cadence and rhythm. Each trad musician has her/his own style and well and being immersed in a particular genre.
Even for non-trad music, like ska or reggae or rock or swing, still listen and note the rhythm and how it is being kept.
Finally, don’t underestimate yourself. One of the best classicist musicians I know is also one the the best trad musicians I know. Some people (where I live in the USA) say he doesn’t play in the true Irish style. But guess what. I was once with him in a pub in County Donegal and the other pub musicians knew him and called on him to play some tunes. And these hardcore Irish were delighted by his playing. Plus he can pick up Cape Breton by ear easily, too. Of course, he is especially gifted, but his example always inspires me, even if I can never approach him in talent. But the talent is not the point; it is his love of trad music (and all music, really) and desire for everybody to have fun that are the inspirations.
Good luck! If you practice and listen, you will start to pick things up by ear more easily. And as far as transcribed tunes, they are useful as guides, but take them with a grain of salt.
