The framing of "what do I owe her" is the wrong frame entirely. You are not buying equity, you are acquiring control of an asset and a below-market debt instrument simultaneously. Those are two separate things and conflating them is why you can't land on a number. The 3.1% loan on a current 30-year is worth real money to you, probably $40,000-$80,000 in interest savings over a 7-10 year hold depending on the balance, so the question is actually how much of that spread you are willing to share with her to get the deal done.
What I would do instead is back into it from her situation. If she has zero equity and is current, she has a reason she wants out that isn't financial upside, maybe relocation, maybe she's tired of carrying it, maybe a life event. Figure out what that actually costs her to walk away cleanly, moving expenses, lease break fees, whatever, and write a check for that specific number. I did something similar on a duplex in Columbus in early 2024, seller needed $6,200 to cover her deposit on a rental in Phoenix and that was the entire conversation. The loan balance was $214,000 at 3.4%, and I was not paying her equity she didn't have, I was solving a logistics problem for $6,200. That is the number you are looking for.