HLS with organic liquids is lab scale not production scale. A combination of spirals and cyclones and possibly final clean with a centrifuge is typically used in production and can separate materials with close SGs. One example that immediately springs to mind is kaolinite (china clay), a fine white substance with an SG of 2.2-2.7, which is separated from mica, a fine white substance with an SG of 2.8-31, using centrifuges.
On the cost front this stage of the process is essentially just pumping. Depending on your power cost is likely less than $2 per tonne.
