Yeah I dug into all this a while back while I was trying to raise my score. Turns out the most productive thing I did was just ask my current cards to up my limit. A couple of them doubled, so it dropped my utilization way down, which shot my score way up. I think I was around 675 and went up to 750 just with that trick. I got into the 800s by paying off the credit cards.
Its an annoying metagame you have to play to get the "good interest rates," but those little tricks can save you a fuckton of money over time.