Hello DeterminedSlacker: This is a difficult situation. And you have clearly thought it over thoroughly. Personally, I agree with you regarding debt. And, I think you are correct. If your gf has already switched majors once & now wants to switch again, what's to say she won't want to switch a third time at some point. And, as a result, the student debt just keeps piling up higher & higher.
Of course you want her to study what inspires her & makes her happy. And realistically, it's her decision. The two of you aren't married. So you're incurring no financial obligation as a result of her changes of major. So, from my perspective, I think all you can do is to express to her basically what you have written here. If she chooses to go ahead anyway, then it's really her decision.
I suppose one possibility might be, if she's willing to do it, to meet with a financial advisor, or credit counselor... someone who can look at your current & projected financial situations & give you some perspective with regard to what the two of you are likely to be facing given your gf's current debt load as well as what you may be faced with if she changes her major again. The upshot of such a meeting might be to either scare her into not making the change, or perhaps it might allay your fears a bit. Right now, you're both working off of hypotheticals. If you can get some real projections down on paper, it may help to make the discussion more concrete. Good luck!