Bobert has it spot on; there is a point when all you have to do is listen to what is being played; the hands translate what you are hearing almost automatically. Practice helps, but there is such a thing as trying too hard with one particular tune. Play lots of stuff, with different sounds and techniques, and eventually various licks will 'stick' in your muscle memory. Most picked tunes have a series of licks, patterns and chord structures which can be found in other songs, and when you come across them your hands will tell you 'I know this, please disengage brain at this point'. Try to practice not thinking about it as you play, and don't worry about odd slips and fumbles. Play the tune, not the technique. Try playing the tune slowly, then much too fast, then slowly again. Each time I do this, my fluency improves on the second slow version.
Last things; judging by the material you are playing, your are very advanced for a player of two years standing. Be proud! You are not too old to be starting an instrument; my dad was 70 when he took up his first instrument (the cello, for God's sake!)and now plays regularly in a small chamber orchestra. He's 84 and still learning. If you want a book on this, 'The Inner Game of Music' by Timothy Gallwey is very good.
Best wishes
Tim
PS I had a gig last night, and I was playing a tune on mandolin that I know inside out...until I started to think about what I was doing!