Alan - how does your post answer the original question about silver solvents? You show that silver carbonate is less soluble in water than silver chloride, but not if it is a silver solvent or not.
Look at silver sulfite - it has a solubility product of 1.5 x 10-14, that makes silver sulfite less soluble than either silver chloride, silver carbonate, and even silver bromide - yet sulfite ion is a silver solvent. Silver cyanide is even less soluble, Ksp = 1.2 x 10-16, yet cyanide ion is a silver solvent.
Formation of a complex is the key to the action of chloride and cyanide as silver solvents.