As Sally said ... just because her name can't be on the loan ... doesn't mean it can't be on the deed.
But be honest with yourself, the headache isn't due to the loan product you chose ... it is because you are playing house with a woman you are not married to and you are trying to determine an equitable distribution of the assets.
This relationship doesn't sound very stable. If each of you want to protect your own assets ... where is the "we" in this relationship? If there is no "we", why did you just become legal partners in a house? (Put her on the deed and you just formed a legally binding partnership)
If you think you are headed toward marriage ... then Don't sweat the option of lost rental income you could have had. If she is like a fraternity brother or a stranger ... charge her rent. If she is a partner, then treat her like family ... since you want to play house with her.