A little behind the scene behind the system that spawned over 200 games
Having played with the original Loot Roll mechanic, having such a wide range where you don't find something useful fits the themes of Zombie Survival / The Last of Us very well. I could see keeping the d20 as the die to roll, while adding additional complications for low rolls and expanding the items that are found.
Maybe something like:
1: Something really bad happens - You find nothing useful. Suffer 1 Stress. Add a complication to the current scene and the next scene.
2-3: Trouble is Coming - You find nothing useful. Add a complication to the next scene.
4-5: Trouble is Here - You find nothing useful. Add a complication to the current scene.
6-9: You find nothing useful. Describe your search in a way that moves the story forward without a complication.
10-11: You get a d4 depletable item.
12-13: You get a d6 depletable item.
14-15: You get a d8 depletable item.
16-17: You get a d10 depletable item.
18-19: You get a d12 depletable item.
20: You Get a Single-use d20 item. Remove it from your backpack after a use.