This is a really fascinating discussion. I was drawn to it because of my own struggles to understand and clarify expectations in my marriage. A few years ago I became closer to a friend and we started writing to each other on spiritual topics. I never planned to leave my wife or engage in anything physical, but she accused me of "emotional adultery". I don't believe I would be upset if the situation had been reversed, but my perspective seems to be less common than hers. I see jealousy as a fear to be overcome, not through being cheated on but through realizing that love doesn't have to be hoarded and that nobody needs to depend on one specific person to supply all of it. I've found love to be the basis of my identity, not something that I have to manipulate or persuade others to supply. This doesn't mean I don't think there was a problem with my activities with my friend, or at least my perspective - I struggle with that, to understand how to truly love everyone right while in the role of a husband. I have enormous sympathy for everyone struggling with these issues, which are not trivial.
I think I understand why mr.buffnstuff is holding on here, even though it would obviously be easier and safer for him to find a new girlfriend. Part of it is the confusion of responsibility - being persuaded that he is essentially responsible for the feelings that his decisions seem to cause, and the behaviors which the feelings are used to justify. This is going to be an endless sinkhole. I don't think the most important thing is whether you stay or leave the relationship. The most important thing is that you connect responsibility and control - a person should be responsible for what they control, and not take responsibility for what they have no control over. I've learned that it is, in fact, possible to "control" my own feelings, maybe not always in terms of feeling them, but in terms of keeping them and their true causes in perspective, retaining awareness of underlying peace and its basis, and especially in terms of being able to choose how I respond. I've been learning to see people and situations that elicit unwanted feelings as teachers and opportunities, and if you can too, maybe this relationship isn't necessarily something to escape. This is hard work, but a massive benefit from taking responsibility for my feelings is that I can let other people be responsible for theirs. This doesn't mean that I have no responsibility for how I treat others, it only means that once I've done the best I know how for them, and learned what I can, my responsibility ends and theirs begins, and seeing that boundary clearly leaves me at peace regardless of how they respond.
But to work on this you have to keep your cool, find peace of mind, retain perspective - and recover your sleep. It is a good sign that you are here asking for other perspectives. Your situation reminds me of when someone goes to rescue someone who is drowning, but in their panic they grab the would-be rescuer and push him under the water, trying to stay afloat. From everything I know of people, you and your girlfriend are both very strong, loving, helpful people, but you have to stay out of fear to be those people. If you can do it, you can teach it.
If I had advice to offer, it would depend mostly on how committed you are. If you have, or had during times of peace, a sense that you and your girlfriend can and want to both grow through this over the long term, I might suggest that you move out temporarily while giving every assurance of remaining committed to the long-term relationship and making time with your girlfriend a high priority - second only to the time you need away from her to compose yourself. If instead you have realized that you were originally expecting things to change in ways you can't control, maybe exploring this will send you apart. But there will always be problems, with another girlfriend, and it can take people amazingly long to want to work on some of their own issues. It was counter-intuitive to me at first, but the fastest way I've found to help is to help people love and trust themselves, not particularly to get them to love and trust me. By themselves I mean their healthy selves or higher selves, and the Source of where those selves came from, not the self-defeating part of ourselves which can't be trusted by definition.