Considering a '67 Dart GT Convertible as my first project. Am I insane?

Welcome. Great car and as you stated yourself it needs more inspection. I feel $7k is too high given the amount of cancer, but a 4 speed vert isn't that common. As stated there are some 67 only parts then there are convertible only parts. So not the easiest for a beginner. How much are you willing to do your self? What is your goal and what is the budget? Are you looking to stay stock or going all out performance or somewhere in between?