I don't know quite how to help you. If you really can't deal with her having other relationships, poly isn't an option.
However, maybe mono isn't an option for her. You should talk about it. I mean I know you say she said she'll be mono if it ends with the other person, but she might be saying that because, like you, she doesn't want to lose you. And she's hoping with time it will work better.
Or maybe she would be fine with a mono relationship but doesn't want to hurt the other woman, just like she told you.
What's the problem with meeting her with your girlfriend also being there? You could always do that first and talk about things and see if you have a better idea what to do. I'm not sure I understand what the problem is, maybe it's scary for your metamour to meet you alone and that's why she'd rather have your girlfriend here too, plus she's who you have in common after all.
I would suggest to try and arrange a meeting with the three of you and get to know your metamour. Then you can see a) if poly is still unthinkable, b) if she makes your gf happy and c) how committed and in love she is, if it's still a stage where she could take it or leave it.
Either way, you'd probably have a better idea after said meeting, whether it goes well or not.