Do not underestimate your importance and the impact you can have for the category 3) students.

My first year Calculus professor 20 years ago had very similar feelings and frustrations, but through his passion he connected with some of us. Lots of great students don't apply to the best schools and for whatever reason end up stuck somewhere close to home. He eventually encouraged me to take his Modern Algebra class and that opened my mind to a whole world of Mathematical beauty.

Enjoy the opportunity to touch young minds as long as you can.