I am actually in the same situation as you, only perhaps worse off. I was naturalized through my parents in the early 90's. My mother remembers that we (my sis and I) were issued separate naturalization certificates and she said those also had an individual number on it, different from hers. We've moved so many times since....both my parents and I to different locations, that somehow our naturalization certificates were lost. My parents have theirs, but we've turned both my parents and my house upside-down looking for my certificate and it is nowhere to be found. Now I'm still at the petition stage so I have a while longer before I get to where you're at. I'm waiting for approval, and I used my passport to prove citizenship. I'm just very worried now as I see someone just posted that they got issued an RFE because they provided their passport instead of naturalization certificate. So I could be looking at an RFE myself, in which case I'm really SOL. I will just have to send them a copy of my mother's naturalization certificate w/ a notarized letter explaining that I derive my citizenship from my mother's naturalization and hope they accept that. (That is my plan if I get an RFE. You think that will work?)
Which makes me think....perhaps you should also have such a letter handy and notarized and sent to your fiance, she can present it if asked. Just an idea.
Sorry to be so long winded....in your case, I don't think you should have a problem...especially if the interview is so short as you say. As long as your financials are in order, you have enough finances to support your SO, you should be fine. I mean the interview at the consulate is the domain of the Department of State, and you already have gone through USCIS (approved petition) to get to the interview. USCIS is who verifies if you are truly the US citizen you say you are. So my gut tells me you should be fine.
Good luck!
-P