Adding a Custom Item to a Mobs Loot Table (Killed by Player)

I am creating a custom set of loot tables for a datapack that I am making for my friend's realm. The idea of the datapack is that it is a custom music disc datapack. The datapack itself handles all of the play sounds, detecting the disc being put into the jukebox and removed from it, loot tables etc. etc. The datapack is accompanied with a resource pack that stores all of the sounds, and the textures, for the discs, using the CustomModelData tag in Optifine to create the customized discs. I have been able to get the datapack and resource pack to play the sounds (using the /give command) but unable to properly integrate it into a custom loot table. The datapack itself already adds the new discs to creeper being shot by skeleton drops, however I would like to add it to a basic stray drop. This is the code I have already set up. This is added as a seperate entry into the mob drop pool for the stray.
{
      "blonus_rolls" : 0.0,
      "conditions": [
        {
          "condition": "minecraft:killed_by_player"
        }
      ],
      "entries": [
        {
          "type": "minecraft:tag",
          "weight": 10,
          "name": "minecraft:music_disc_11",
          "functions": [
            {
              "function": "minecraft:set_nbt",
              "tag": "{CustomModelData:1, HideFlags:32}"
            },
            {
              "function": "set_name",
              "name":[
                [
                  {
                    "text": "Ocarina of Time",
                    "color": "blue",
                    "bold": "false"
                  }
                ]
              ]
            }
          ]
        }
      ],
      "rolls": 1.0
    }