That firm recruiting and job hunting -- far from being some mystical combination of factors that you can precisely game from the outset -- is all about getting as many interviews as you can, and then just being affable, polite, engaging, and following the interviewer's demeanor/social cues.
Grades are just another way to get more bites at the apple (ie, interviews). Networking is just another way to get more bites at the apple. Mass-mailing is just another way to get more bites at the apple. No matter how strong your grades, no matter how good your contacts, no matter how charming you think you are one-on-one, just keep throwing everything you have into getting more interviews, because it'll all come down to where you click or not.
I saw friends with grades well below median walk out with offers from firms that other friends with high grades didn't get a callback to (and vice versa), and it really does come down to fit. Some firms are uptight, some are very laid back; some nerdy, some hardcore bro-y. It's nearly impossible to tell until you go in and meet them, and you may well -- as I did -- walk out of some callbacks thinking "good lord I would never want to work with these people" even if you thought the firm was perfect on paper going in. You may well -- as I did -- end up getting and accepting an offer from a firm you knew only by reputation but ended up clicking perfectly with everyone in it. I'm in a small high-profile east coast market and I have friends who are working at peer firms right now and I can tell that each of us have personalities that strongly align with the personality of our respective firms. It wasn't about who had the best grades or the most prestigious resume. It really came down to where we fit in.
So: no matter where your grades are, how great your softs are, how good your WE is, how many bid slots you have, apply apply apply. Mass mail. Call every favor. Pursue every connection. Do whatever it takes to get your butt into more interview seats. Be yourself, but be polite, earnest, and affable, and you'll find a firm that clicks with you (and vice versa). It's almost impossible to know which one that will be before you go in and meet them, so keep an open mind. But that's really all it takes, and all it comes down to.