"Is there some sort of process we could use to clean up used engine oil, to remove all the metals, additives, carbon, and other stuff to turn it back into straight mineral oil?"

Got this off of the API webpage:

Reprocessing is the most common method of recycling used oil in the U.S. Each year processors treat approximately 750 million gallons of used oil. Seventy-five percent of used oil is being reprocessed and marketed to:

43% asphalt plants;
14% industrial boilers (factories);
12% utility boilers (electric power plants for schools, homes, etc.);
12% steelmills;
5% cement/lime kilns;
5 % marine boilers (tankers or bunker fuel);
4% pulp and paper mills;
>1% commercial boilers (generating heat for school, offices, etc.);
5% other.

Re-refining
Fourteen percent of used oil collected is turned over to re-refiners who return used oil to its original virgin oil state.

Re-refined base oil is the end product of a long process involving used oils. The oils are first cleaned of their contaminants -- such as dirt, water, fuel, and additives -- through vacuum distillation and then hydrotreated to remove any remaining chemicals. Finally, the re-refined base oil is combined with a fresh additive by the blender to make the finished lubricant.

Used oil can be re-refined over and over again, and is subject to the same stringent refining, compounding, and performance standards as virgin oil. Before buying a motor oil product, check to see that it has the API Service Symbol "donut" (which identifies the performance level, viscosity, and energy-conserving properties) and API Certification Mark "starburst" that tells you that the product you are buying has met all the current performance specifications established by the oil industry, and the vehicle and engine manufactures.