I have this same problem. I was in a LTR for 7 years, and during that time, I had a MASSIVE
social circle. Because of that, I know lots of girls that I've never talked to on a gaming/more than friends level. Since then, I've had some success with girls I already know (I'm dating one now) but for the most part, the friend zone is like quicksand. The harder you try to get out, the deeper you sink. A lot of it depends on how well you already know the girl, how close you've been previously, and how long since you've seen her. If you have hung out a lot, been close, or seen her recently, it's a lot harder. The girl who I'm dating in that category I've known for a while, but she doesn't live in my town anymore and I started gaming her after I hadn't seen her for over a year. IME you're much better off gaming girls you don't know already. Either way, though, the key to staying/getting out of the friend zone is
KINO. Good luck, man.