To answer the original question, "Would you ever draw your knife instead of your gun?" Yes. Once in an elevator in Massachusetts, I wished I could have.
I was in Massachusetts, in an isolated parking garage, in the elevator, legally carry my handgun (strange things do happen) when two scruffy looking men entered and gave me and my wife a very long, very careful look. At contact distance, with two dangerous looking characters, with my wife stuffed inside a metal box with me, I REALLY wished I hadn't left my Sypderco Police Clipit at home. I WAS armed with a custom .357 magnum. Had we been attacked, I certainly could have used it, but from that day forward, I started thinking of my knife as my primary weapon (because it is ALWAYS with me) and my handgun as the backup (because it is SOMETIMES with me). I still think this way.
PS
When carrying a handgun, I like to keep my legal length folding pocket knife in a--of all places--a pocket. That way, if I feel threatened, I can casually rest my hand on the knife. No harm. No foul. I find this practice helps control my blood pressure.