I have tried a few leather straps and the OEM sail cloth that all were fine on the LLD, but never perfect. I also have tried lots of pull throughs, but it took me until a month ago to try a perlon... I had a feeling it might work and it really nails it! This is just a £6 job from Ebay and really does work a treat for me - the texture adds to it but doesn't add more clutter.
I think the new OEM mesh that now comes on the LLD probably makes it all seem to shiny!