there is at least one prof there who clerked for O'Connor, so you never know. She's pretty moderate.
Yeah, but she's also pretty retired, too. 
This is true, but I was just using her to point out that not all the connections are with the ultra-conservatives, so hope is not lost for the moderates/liberals.
The thing is, though, those connections probably change with the membership of the court. Remember, you're not exactly applying to the Supreme Court as an institution; you're applying to an individual justice, who has his/her own idiosyncratic preferences, his/her own ideal characteristics for what makes a good clerk. The fact that certain schools dominate the race for these positions, while others of similar rank do not, is likely only a reflection of a justice's reserving a special place in his/her heart for graduates of that school.