EEE is a fine grit polishing compound meant to basically finish the job on bare wood where regular sandpaper leave off. If you apply it to a finish such as shellac or varnish, it is sort of like sanding the finish with an extremely fine grit so it is not surprising that a sludge was created. Shellac is soft and the heat generated during friction polishing can easily make a gummy mess especially since the fine particles of the EEE compound will become embedded in the softened shellac. You can probably get away with hand applying a polishing compound to shellac since not much heat is generated and you can more easily control the amount of pressure being applied. I have had much better success hand polishing using Micromesh with water as a lubricant. It is slow but can create a glass finish for special pieces. Personally, I would not go to a finer grit polish on the finish than what I used on the bare wood.
BTW, I have EEE, white diamond, and all that mess and essentially do not use them any more.