If as you say the full organ is in a right hand voice, it must have been assigned to R1, or 2 from the OTS of the style. (If you have the OTS link button ON, OTS 4 will set this voice automatically when Variation 4 is selected.)
So to change it you need to modify the OTS, eg find the organ in R1,2 and either lower the full organ volume or change it to a different voice and readjust volume to suit.
Now save your new settings by pushing memorize followed by the OTS button you want to save it to (presumably OTS 4?).
Follow the on screen prompts to save the style including the changed OTS.
Note this is a different procedure from simply saving the style, which will save the style parts but not OTS.
John