How can the Supreme Court escape from the perception that it's partisan?

Lawprof Barry Friedman is working on the theory that people have lost trust in the Court (or so the polls show) because they perceive the Court as political. (Friedman stresses that politics is different from ideology, ideology being something one actually believes in.)

Okay, so if the Court cares about the public's disapproval and wants to do something about it — which would be, ironically, political — then the Court should work to deflect the perception that it is political.

Well, then, the question becomes why do people perceive the Court as political? One answer is: Because it is political. In which case, people should be congratulated for their perceptiveness. Nice going, people. You are not dupes. But that's me saying that.

What Friedman is saying is that certain cases are making people see the Court as political. What cases?
Basically, Citizens United. Why do people think the Court is political because it valued free speech rights above a congressional effort to squelch speech 60 days before an election? Because elite lawprofs like Friedman have been telling people over and over that Citizens United was political, and you know how much people trust elite lawprof commentators... manipulating the perceptions of American people since... never.

Let's back up a minute. Citizens United came in 2010, the year that "marked the beginning of the current downward slide." Here's something else that happened in 2010: Elena Kagan joined the Court. The year before, Sonia Sotomayor joined. 2 Obama appointments in 2 years. Friedman talks about those 2 appointments, but only in the context of saying that after Kagan replaced Justice Stevens, it became true for the first time since 1953 that all the liberals are appointees of Democratic Presidents, and all the conservatives are appointees of Republican Presidents. (Stevens had been appointed by Gerald Ford and, Souter, whom Sotomayor replaced, had been appointed by George H.W. Bush. You have to go back really, really far to get to a Justice who went conservative on a Democratic President!)

Friedman concludes:

The more justices are seen as making decisions on partisan issues and the more cases are decided along the current 5-4 Republican-Democrat divide, the more the public will disapprove. 

See how that works? There are 5 conservatives and 4 liberals. The liberals, though they are the minority, need to win a whole lot more if the Court wants to recover the approval of the people. And that — if the Court were to buy it — would shift the Court to the liberal side without needing another appointment.

But here's the test of Professor Friedman's actual belief in his theory. What if President Obama gets the opportunity to replace one of the 5 conservative Justices? Would Friedman publish an op-ed pressuring the liberal Justices to vote with the conservatives in order to bolster respect for the Supreme Court? Or would he be cheering hooray for the liberal majority?

Oh, it's not that I think he (and his fellow elite lawprofs) would publish op-eds saying that out loud. I just think we'd be flooded with academic-sounding praise for all the thoughtful, well-reasoned opinions.