If you are selecting styles manually, freezing can be used, but yes, the way Yamaha chooses to group left voice and a number of other properties with the style can be very restrictive sometimes. But they continue to keep with their old conventions in their latest keyboards in spite of it.
Creating registrations (eg. using voice setups taken from OTS's) to switch voices and styles during playing would give you more flexibility if you consider the extra work needed would be worthwhile.
John