I think you're wrong. The three elements of unjust enrichment are satisfied and oral agreements, especially between domestic partners , are valid. Anyway, I hope she sits down with me and a mediator before this gets into litigation. However, I doubt it. She's a woman.
Some oral agreements are valid between domestic partners... they are simply not treated in any way more sacred than oral agreements between any two people. Additionally, purchases of interest in real estate must be in writing. I believe your case has some merit, but the portions given towards starting up via the gift letter, and towards the house may well be lost if the matter moves to litigation.