Unless I interpret your post wrong, it sounds like you do not have enough bow (relief). The neck is too straight (truss rod too tight) and the string touches when you hold it down, the neck is definitely too straight. I think you need to loosen the truss rod just a bit to add some relief or bow by turning CCW when viewed from the peg head. I only adjust truss rods one "flat" at a time, and keep track of how many flats I've turned. An Allen wrench has six sides or "flats", so I adjust by 1/6 turn at a time. One or two flats is usually enough to make any adjustment I want.
I have the truss rod adjustment tech sheet on my computer. I was going to post a link here, but the Taylor web site is off line right now for upgrades. Ping me with an email at noisebuster@gmail.com, and I can send it directly. The pictures make this all much clearer to understand. The tech sheet says that you should have 0.01" or the thickness of a business card between the 6th fret and the string when fretting at 1 and 14.
