Oh how I can empathize. I was in almost the exact same situation about 8 years ago, with my wife. It was a rough patch, but we eventually worked it out. I will tell you my story, because I hope that it will help you in your own life.
I was raised Mormon (they're very conservative, I am no longer religious). While dating I had told my wife that I looked at pornography, and probably always would. I knew that a lot of marriages had been hurt over conflicts about porn, so I made this very clear. She said she didn't care. Really, she just assumed that once we were married, I would not be attracted to any other women and wouldn't want to look at the porn anymore.
When we were married, and I was still looking at porn, she got upset and we argued about it. I agreed to speak to my bishop about it and try to give it up. At about this time she became Mormon too, and started taking Matthew 5:28* literally. If a girl in a short skirt walked by, and my head turned, we would fight. Then it escalated. I would just be walking through Wal-Mart looking dead ahead, and if a skirt went by in front of me, and she thought my eyes twitched, we would fight. I stopped going out, for fear of seeing anyone that might arouse me. She took the covers off of her work out videos, so I wouldn't see the women on them. It got bad. We fought constantly, and almost never had sex. Note: She is a wonderful woman, she just took a detour through crazy land for a little while. To be fair, I wasn't the healthiest person either.
To defend 'my side' of things, I did a lot of research. I learned that vision enters your brain through more than one path, and that you're brain has already decided whether or not something is arousing before you even see it consciously. This, and other research into male sexuality taught me that It is almost as hard to change what arouses you as it is to train your heart to beat in morse code.
If she wants a man who looks at all of the women in the world, and thinks she is the only one that is sexy, she is living in a fantasy; that will never happen.
I made a lot of arguments. I explained the physical reality of arousal as described above. I told her that "I can't control what I want, I can only control what I do, so only what I DO matters." I told her it was like she was chocolate cake, my favorite, but if you never taste anything else it gets bland. (She HATED being compared to food, it really pissed her off, so use that one at your own risk.) You could compare it to any other form of enjoying beauty. You have a favorite song, but you still enjoy listening to others. It sounds like you have already tried some of these 'reason-based' arguments, and they have not worked. They didn't work for me either. It sounds like your GF dismisses these arguments; my wife just fell back on religion saying that it didn't matter what arguments I have, God is still right.
This went on for a little over a year until I left Mormonism. She left it as soon as I did, and it became clear that the real issue was her need to feel loved, special, and secure. She realized that she had been unreasonable while trying to get those needs met, and we talked about how to meet those needs without trying to change who I was as a person. It was this approach, talking about the feelings and our needs, that fixed it, not the logical explanations or analogies.
I would advise you to sit down with her and explain that being aroused by pretty women is part of who you are, and that you need someone who will love you for who you are. Don't make it about right or wrong, should or shouldn't, make it about what you feel , what you need, and what she needs and feels. Find ways to help meet her emotional needs without compromising who you are.
Also, if you are willing to be monogamous for her, then I would not push the poly thing much right now. Definitely tell her about it, and tell her it is something you are interested in, but if she is this jealous and insecure with just you looking at other women, pushing the issue might really trigger those negative feelings in her too much right now.
Well, I know it was long winded, but I hope you can get something useful out of it. Best of luck, I'm rooting for you!
*"But I tell you that anyone who looks at a woman lustfully has already committed adultery with her in his heart." Come to find out this is a terrible way to interpret the original Greek, as the original statement bears almost no resemblance to what this appears to say, but that is a story for another time.