1.) Organics DO build up in large aqueous volumes and necessitate removal. TBP has its own set of problems as it ages anyway. Alkyl sulfides will gradually oxides to alkyl sulfoxides, which are much more soluble in aqueous feeds but yet coordinate precious metals. Even dibutyl carbitol...the solubility you quoted is in water, not in strong acid milieu and it's actually 3 g/L. I'm well familiar with leach recycling--we use this technology and I'm telling you, it's no magic bullet. If you wish to make a thread on solvent extraction, please do so (in fact, make it by metal, i.e. S/X of Pt, S/X of Pd, S/X Au, and so on) and I will gladly participate. I might be the only participant in that thread, but I've done SX on Pt/Pd/Ir/Rh/Au both lab, pilot, and process in the case of Au.
As to the original post:
Silver refining of feeds over 80-85% wt silver are best done in an electrolytic silver parting cell. The two methods you quoted do not work well because 1.) cemented silver often contains copper impurities, 2.) silver chloride generated Ag2O contains other impurities that are stuck onto the precipitate and difficult to remove. Both of those methods should be looked at as a preliminary upgrading step. There is a method using sodium formate for silver refining that can yield 4N silver, but not if palladium or nickel is present, which contaminates the silver. To remove those, either a cell with good electrolyte pH control, or dissolve in nitric acid and heat until the oxides of these metals form, then cast the silver nitrate onto hot stainless pans like peanut brittle, break up and dissolve in UHP water, let settle, decant, then formate. That silver will be in excess of 6N.
Lower grade feeds can be melted and upgraded in a reverberatory furnace with excess air and some flux to produce a slag rich in copper and impurities, that can be sold to the copper refiner when you have a semi truck worth.
Feeds less than 40% Ag by weight should be melted with copper and sent to the copper smelter or, if in small quantity, used to cement out silver from contaminated cell baths.