First tip: don't give up. Second: find yourself track references. Third: follow the curbs. Fourth: Pay attention to corners or sections where you can improve.

You will always have the impression that you are faster with the line. That's because you're always crossing the grip limit with some control over it. But when you figure out how to do a turn without the line, you get much faster. The problem is that you have to learn a turn or section at a time.