Scott, I’m so sorry to hear what you are going through.
First of all, it’s not your fault that she chose to cheat. It’s fine to accept some responsibility for the condition your relationship, but the choice to have an affair is hers and hers alone.
I think you have read the situation correctly. She knows what she’s doing is wrong. She’s seen your agony over the past two months. She wants the story to be "Scott and I decided to see other people", not "we broke up because I cheated." She also wants you around to help pay the bills and be there as a fall-back plan. Seeing other people is the opposite of resetting your relationship, it’s breaking up and being single.
Since you know what the pick me dance is, you know better than to do it, as it will only serve to exacerbate your misery. Since you don’t want to do that, and you don’t want to co-habitate together as colleagues while you date other people, that leaves you only one option.
She’s not going to end her A, and unfortunately there’s nothing you can do to make her. The people that get themselves out of infidelity do it by taking control. They become the deciders. They say, I will not stand to be treated this way, and start taking steps to end the relationship.
For your emotional health, learn the 180 - read this and make sure to read the FAQs. https://www.survivinginfidelity.com/documents/library/articles/discovery/understanding-the-180/
Speak to a lawyer or two on Monday. Google just told me that Oregon does not recognize common law marriage. Understand your rights and responsibilities. Is the house in your name only?