First, Jew-lo is ABSOLUTELY correct on all accounts. Even as psycho as it sounds, some women think that way, it's the real women who can understand that thought process but don't subscribe to it.
But, after all that I don't have much to contribute except one thing. I know that b/c you still care for the girl you want to be there for her and all, and also people are suggesting the "friends w/benefits" thing, but I think that you care way too much for her for that to work. Unfortunately you have to cut ties with her---completely, in order for you to get over her. There's been a suggestion that for every year you were in a relationship with someone you need 6 months to get over them. (Believe me it works) But your 6-month or more period hasn't even begun b/c you've kept in touch with her. And I know it may seem mean even cruel considering her situation but it's the best for YOU and all that other stuff is her problem to deal with.
But continuing to sleep with her still surrounds you with her "aura" "spirit" ----whatever you choose to call it, but you can't get someone out of your system that you care for if you remain in a physical relationship with them. And if you want to completely move on with your life and not be stuck to this "bag lady" you've gotta cut all ties.
Hope this all makes sense, good luck.