You forgot AD Katarina.
Haven't played AD Katarina in a while. Might try it later.
Beserkers or Mercury Boots-Warmogs-Bloodthirster-Phantom Dancer-Infinity Edge-Bloodthirster seems like it'd be the best build for her. Not sure how resilient that would be, may have to substitute a damage item with a Sunfire Cape.
Man, you...you like Katarina...
I like Katarina as much as Egoignaxio likes Kennen. Think I have over 200-300 games played as her.