I agree with you, in principle. Long distance relationships are lonely, and for us to hook up on the side would not only be copesetic, it would be logical.
Unfortunately, women just don't respond the way you suggest. If I said to her, 'what do you want from/in me?' I would get a fairly confused, convoluted, and evasive answer. If I pursued, she would retreat. So, I'm afraid it's a moot point.
My only course of action at the moment is to retreat, myself. Catching and/or calling her in her game would only cause distaste. Offering her an ultimadum would prove useless.
I just wish it didn't pain me emotionally to hang out with her, as my journey home each time is one of distaste from her lack of definitive reciprocation. She is really my only solid friend in the city, as I just moved here less than a month ago. A friend like this, though, causes more pain than enjoyment.