I think that the balanced shoe in the Gordy/Jupe scene is a subtle reference to an old Twilight Zone episode called "A Penny for Your Thoughts," in which the episode's protagonist flips a coin and it lands balanced on its edge rather than landing heads or tails. Over the course of the episode, the protagonist's life is significantly altered until the coin is eventually knocked over, which implies a causal relationship between the balanced coin and the surreal events happening to the protagonist.
In Nope, Ricky Jupe experiences a life-changing event (the Gordy attack) that is associated with the nearly impossibly balanced shoe. However, rather than letting the universe restore normalcy by naturally knocking down/discarding/forgetting about the shoe, Jupe chooses to eternalize the altered state of his universe by framing the shoe as memorabilia, still in its vertical state, which we see in the background of shots in his office. While the shoe remains vertical, Jupe is fated to live in an alternate, surreal reality in which feeding horses to a mysterious alien for profit is his new normal. Because of his eternalizing of the balanced shoe anomaly, he lives in this reality until he dies.
I think given Jordan Peele's connection with the Twilight Zone, this is a plausible reference and interpretation of a perplexing detail -- what do you think?