The first thing you should do is get your resume screened and reviewed by an expert. Sometimes it's not about the content but the way you're telling the story. We have selected quite a few people at McKinsey for interviews with low GPAs because their resumes stood out in other areas. I'm happy to work with you on that if you prefer.
A referral alway helps. It doesen't always have to be a Partner/AP. Even EMs hold weight in these decisions.
Finally, I think it's good to have a few cases under your belt and know where your gaps are, but you don't need to wait till you're '100% ready'. Remember perfection is the enemy of getting things done! ;)