Any advice on how to clean my flylines?

I usually soak them in some warm sudsy water, rinse and follow up by running them through a commercial 'line dressing' tool(two felt blocks in a little plastic case.)

The problem I am having is that there is still a lot of gunk on the line. They seem to get clean only on the top and bottom that are in direct contact with the felt pads. The sides still show a lot of grime.

These particular lines are of a light color, maybe they just show more dirt? The lines in question are RIO Windcutter brand and are light yellow in color.