I haven't had a chance to read all of the responses so I don't know if someone has said something similar to what I have to say, but I think you're in quite a pickle Mr. Positive.
You want a relationship with this woman, but the more you force a relationship on her, the less chance there is that one is going to arise. Of course, if you sit back and let things ride as they are, there is a much better chance of an LTR coming about. If you try to have a "relationship talk" with her, she isn't going to respond well and give you some sort of response about not being ready for a relationship or not having time for one - some B.S. response like that.
My advice to you is to sit back and just enjoy things as they are. There's no need to put some sort of girlfriend tag on her. You enjoy sex with her, you're enjoying the time you spend around her and you hang around with her all the time. And on top of all that, you're not exclusive so you can date around.
I'm failing to see the downside of your situation.
When I've been dating or spending time with a girl I like a lot, and I feel like I could be in an LTR with her, I very rarely bring the subject up. Because, from my experience I've learned that "relationship talks" rarely end well. If an LTR does actually come out of it, the girl immediately holds the frame and the power in the relationship.
Don't force anything on her. Just sit back, chill and enjoy her company