I think this close, but a little off. Work hard only on what matters. Join the high visibility projects and work hard on the important parts. "Nobody notices" -> that's up to you. Document and demo your achievements every few weeks.
Work only the good jobs. If it's not good, switch teams ASAP. Never, ever wait for "things to improve". So many times after I switched jobs, I said to myself "Man, why didn't I leave sooner?"