I was just like your wife until a few weeks ago - terrified of a chimney fire. That's because we had a fire last January, and it was one of the scariest things I've ever experienced.
Insurance paid for a new wood insert and new sleeve up the existing fireplace chimney. (FYI, our chimney also had two 90 degree angles in it, which the install guy and insurance agent said was a huge no-no, and against code here in NY. So I agree with the other responses that that should be replaced with either straight or 45's.)
Until a few weeks ago, I was always shutting down the damper when we hit 300 degrees, out of pure terror. And my husband was letting me get away with it!! Plus our wood wasn't the best.
A few weeks ago we had the chimney cleaned and it was full of scary gunk.
So I've done a LOT of research in recent weeks, including coming here for some awesome advice.
What I've learned, loud and clear, is this: The hotter the fire, the SAFER you are!!
It seemed counter-intuitive to me, but once I researched everything it made perfect sense.
Please tell your wife that I used to be just like her....terrified. And she needs to either take your word for this, or get on the Internet and this forum, and research it for herself. Or have her talk to the folks at the hearth store or the chimney sweep - ours was very informative and really helped to put me at ease.
FYI, when our chimney looked about as gunky as yours, we simply didn't burn at all until we had it cleaned. I think your wife is right that a hot fire right now, with that much creosote, could spark a nasty fire. Just my .02....