Documentation with me indicates the Shell Sulfinol X mixed solvent may be suitable for this ( MDEA - piperazine - sulfolane - water) for RSH and H2S removal, if the activated MDEA option ( MDEA - piperazine - water only blend) doesnt cut the cake. If heavy hydrocarbons co absorption is an issue with sulfolane, switch out sulfolane with Selexol. The Sulfinol X process is proprietory to Shell.
Obviously, if you could chill or cool this gas somewhat before the absorber, that will help to knock out the heavier RSH components and the heavy hydrocarbons too, and reduce the heavy HC co absorption associated with sulfolane.
Obviously, a split feed of lean solvent to the absorber may be another option to investigate with any of the solvent options mentioned.