"no! Not that but-" boooooommmmm!!!!!
Hell to the No on that second idea. The second approach makes you come off as needy and coming from a position of scarcity. She will see this, and she will lose interest in you because she sees you as someone who will always be dependent on her. Also, charging in head first is a bad idea because you will scare her and make her think you are creepy.
So far, it sounds like you're on the right track. Your first idea of backing off is a great idea and usually the right approach. I wouldn't say to necessarily go boring though. Limit your responses to about 20 words or less, and let her try to get you engaged. Also, add some spontaneity with your response times. One message reply within two minutes. Another one, 20 minutes, or even an hour. Make her unable to guess when you're about to get a message back from her. This also shows her that you're busy and have some form of a life.
Another thing you can do is hit her with some interesting conversations. Generic questions will only get generic answers, and women hate that. Hitting them with a topic out of the clear blue throws them off guard and forces them to really engage in the conversation.
The most important thing that you have right now is the "I don't care mindset". As long as you maintain this mindset, it makes you more relaxed and able to socialize and play with her with ease. The moment where all of a sudden you really want her, that's where most men just fall apart in an instant.
Stay strong, be smart, and may the force be with you.
"There is no better than adversity. Every defeat, every heartbreak, every loss, contains its own seed, its own lesson on how to improve your performance the next time." - Malcolm X