I got interested in how they separated the capsaicin from the pepper sauce.
I had to look up the Soxhlet extraction process.
It got me thinking... I bet the excess water in the pepper sauce would play hell on the extraction. The water should accumulate in the collection pot, which should affect the solubility.
I'd have been tempted to use something aromatic like benzene, toluene, or xylene. You can modify the condenser to separate out the water, which should make the extraction more efficient.
I can see why the methanol was so much more efficient than the ethanol. Anytime you're boiling ethanol/water, you're going to have a lot of water boiling up with the ethanol, which will probably make the extraction go more slowly. If you're boiling methanol/water, the vapor stream is more concentrated with methanol, so the extraction pot is seeing less water.
It worries me that their extraction method yields a supernatant solution. This could be due to the water accumulation in the extract knocking the capsaicin out of solution, which could of course totally mess up the results.
It makes me wonder if benzene combined with a modified condenser (to separate out the water) would yield a regular solution, instead of having solids (which could be some of your capsaicin) that need to be filtered.