"How can a mid-level leader positively influence the behavior of upper-level leadership? Or put another way, how may I more effectively 'manage up' to shape the attitudes and policies of my superiors to create a more effective service cult?"
Years ago, Stephen Covey wrote, "Be an island of excellence in a sea of mediocrity." Keeping that in mind when it comes to influencing "superiors," nothing is more potent than results. Your bosses, especially the senior leaders, will have a hard time ignoring successful outcomes. It's their obligation to see what is working well, why it's working well and share those learnings across the enterprise.
So, specifically, with any idea or initiative you have, pilot it within your department first and track the success, then it becomes more likely to influence those whom you report to.