Everything works other than small oil refinery and BBQ. Found an old thread that said the name for oil refinery is refinery_small_deployed, but neither that or small.oil.refinery work. BBQ just doesn't work at all either. Any help appreciated.

{
  "Permission": "quicksmelt.use",
  "Use Permission": false,
  "Speed Multipliers": {
    "furnace": 10.0,
    "refinery_small_deployed": 100.0,
    "furnace.large": 10.0,
    "campfire": 1.0,
    "BBQ": 10.0
  },
  "Fuel Usage Speed Multipliers": {
    "furnace": 1.0
  },
  "Fuel Usage Multipliers": {
    "furnace": 1,
    "refinery_small_deployed": 1,
    "furnace.large": 1,
    "campfire": 1,
    "BBQ": 1
  },
  "Output Multipliers": {
    "furnace": {
      "charcoal": 1.0,
      "metal.fragments": 1.0,
      "sulfur": 1.0,
      "metal.refined": 1.0
    },
    "refinery_small_deployed": {
      "lowgradefuel": 1.0
    },
    "furnace.large": {
      "charcoal": 1.0,
      "metal.fragments": 1.0,
      "sulfur": 1.0,
      "metal.refined": 1.0
    }
  },
  "Whitelist": {
    "furnace": [
      "metal.ore",
      "sulfur.ore",
      "hq.metal.ore"
    ],
    "furnace.large": [
      "metal.ore",
      "sulfur.ore",
      "hq.metal.ore"
    ],
    "refinery_small_deployed": [
      "lowgradefuel"
    ],
    "campfire": [
      "deermeat.raw",
      "chicken.raw",
      "humanmeat.raw",
      "fish.raw",
      "bearmeat",
      "wolfmeat.raw",
      "meat.pork.raw"
    ],
    "BBQ": [
      "deermeat.raw",
      "chicken.raw",
      "humanmeat.raw",
      "fish.raw",
      "bearmeat",
      "wolfmeat.raw",
      "meat.pork.raw"
    ]
  },
  "Blacklist": {
    "furnace": [
      "deermeat.cooked",
      "chicken.cooked",
      "humanmeat.cooked",
      "fish.cooked",
      "bearmeat.cooked",
      "wolfmeat.cooked",
      "meat.pork.cooked"
    ],
    "furnace.large": [
      "deermeat.cooked",
      "chicken.cooked",
      "humanmeat.cooked",
      "fish.cooked",
      "bearmeat.cooked",
      "wolfmeat.cooked",
      "meat.pork.cooked"
    ],
    "campfire": [
      "deermeat.cooked",
      "chicken.cooked",
      "humanmeat.cooked",
      "fish.cooked",
      "bearmeat.cooked",
      "wolfmeat.cooked",
      "meat.pork.cooked"
    ],
    "BBQ": [
      "deermeat.cooked",
      "chicken.cooked",
      "humanmeat.cooked",
      "fish.cooked",
      "bearmeat.cooked",
      "wolfmeat.cooked",
      "meat.pork.cooked"
    ]
  },
  "Smelting Frequencies (Smelt items every N smelting ticks)": {
    "global": 1,
  },
  "Debug": false
}​

You need to use the rust shortnames 

https://www.corrosionhour.com/rust-item-list/

Also the code is case sensitive so BBQ won't work, it needs to be bbq.

Has to be bbq.deployed and for the monument bbq's its bbq.static. Same for the refinery. Too lazy to test, do we need to add shortnames too, in my config i'm adding them just in case so example for your config: 
  "bbq": 10,
  "bbq.deployed": 10,
  "bbq.static": 10,
  "small.oil.refinery": 10,
  "refinery_small_deployed": 10,
  "small_refinery_static": 10