Image 1. Starting point. Image 2. First clean using old home recipe, removes worst of the black stuff. Image 3. The final after buffing and polishing. I have the glass globe somewhere, I think in my attic.
Nice job on what I think will be a TL11. In relation to your home recipe which has done a good job, I have seen some quite strong acids that give similar results but should not be used due to high risk. If your old recipe does not involve them, then it would seem a very good home recipe. My preference though is vinegar or citric acid being much safer. Anyway, you have a very nice lamp there.
I use vinegar and salt, flour can be added to get the mixture to stick in awkward places, I check it every half hour.