The development of effective methods for obtaining monochiral single-walled carbon nanotubes (SWCNTs) is necessary to make many applications based on them viable for everyday use. Large-diameter semiconducting SWCNTs are particularly valuable due to their low band gap, but the isolation of such SWCNTs remains difficult to achieve as the number of possible chiralities scales strongly with diameter, and there are an overwhelming number of large-diameter SWCNT types. In this study, we demonstrate how monochiral (8,6) SWCNTs, which are 0.966 nm in diameter, can be straightforwardly harvested using the aqueous two-phase extraction (ATPE) method by employing a combination of ionic and non-ionic surfactants. The universal nature of the devised technique was demonstrated by generating fractions enriched with (8,6) SWCNTs starting from various commercially available mixtures of SWCNTs with drastically different compositions. To demonstrate the practical utility of the generated material, we studied how the obtained pure SWCNTs may be chemically modified to improve their optical characteristics. Interestingly, the course of the functionalization was highly dependent on the type of dispersant used to suspend the purified SWCNTs in the aqueous medium.