How to use wrapProgram with Crane

I am writing a flake to build a Rust program I am writing which uses crane. I need it to set an environment variable to set the location of the gstreamer plugins. I’ve tried to use wrapProgram, but it seems to produce no effect (I added dbg! statements to the top of the Rust program to print the value of the variable.) My flake is as follows:

{
  description = "A terminal music player";

  inputs = {
    nixpkgs.url = "github:NixOS/nixpkgs/nixpkgs-unstable";

    crane = {
      url = "github:ipetkov/crane";
      inputs.nixpkgs.follows = "nixpkgs";
    };

    flake-utils.url = "github:numtide/flake-utils";
  };

  outputs = { self, nixpkgs, crane, flake-utils, ... }:
    flake-utils.lib.eachDefaultSystem (system:
      let
        pkgs = nixpkgs.legacyPackages.${system};

        craneLib = crane.lib.${system};

        aoede-crate = craneLib.buildPackage {
          src = craneLib.cleanCargoSource (craneLib.path ./.);
          strictDeps = true;

          nativeBuildInputs = with pkgs; [ pkg-config makeWrapper ];

          propagatedBuildInputs = with pkgs.gst_all_1;
            with pkgs;
            [
              glib
              gstreamer
              gst-plugins-base
              gst-plugins-good
              gst-plugins-bad
              gst-plugins-ugly
              gst-libav
              # Add additional build inputs here
            ] ++ pkgs.lib.optionals pkgs.stdenv.isDarwin [
              # Additional darwin specific inputs can be set here
              pkgs.libiconv
            ];
        };
      in {
        checks = { my-crate = aoede-crate; };

        packages.default = aoede-crate // {
          installPhase = ''
            wrapProgram "$out/bin/aoede" --set GST_PLUGIN_SYSTEM_PATH_1_0 "${pkgs.gst_all_1.gst-plugins-base}/lib/gstreamer-1.0"
          '';
        };

        apps.default = flake-utils.lib.mkApp { drv = aoede-crate; };

        devShells.default = craneLib.devShell {
          # Inherit inputs from checks.
          checks = self.checks.${system};

          packages = with pkgs; [ git ];
        };
      });
}

Any help with how to set this environment variable would be greatly appreciated!