Dragging selected text using the Three Finger gesture
After selecting the text, place your three fingers on the trackpad and don't drag for a half-second or so. Then, slowly drag your fingers until you see the I-beam cursor turn into the mouse pointer. Then you can three-finger drag normally. 

When using click and drag for text, you need to hold the click for a half-second or so before the system realizes you want to drag the text instead of selecting it. This procedure replicates that with the three-finger drag gesture. (As you get better at this place-hold-slow-fast gesture, you can speed it up to a point where you're comfortable with the speed and it still works.)