Hi Bora,
I have had the same problem with some LP BAG (<edit) straps and replaced them. My favourite is a Tamrac with a suede-leather pad on it. They make them for cameras and bags--2 different straps.
Sorry, I don't have a link.
(I also have an assortment of Think Tank bag straps, and LowePro bag straps. I hate having slippery straps that I need to hold to keep a bag or camera on my shoulder. The Tamrac was inexpensive, and works better.)
UpStrap makes a bag strap; I have not tried theirs.
I have added Domke Postal Pads to bag straps that are uncomfortable; I also have added Billingham Pads to my Billingham bags. They work well. I live in Canada. The cost of the Domke PP is extremely high here. I ordered all but the BillyPads from B&H or Adorama when I needed something else, to keep the shipping costs in line...