Have you tried boiling it? Seems I heard of this a while back. Supposedly will take some of the stiffness out. Never tried it myself so if you were to give it a shot I'd try a small section before tossing a whole harness in.
I tried this with a small sample and had no luck Jim. I also tried a few different solvents with no results as well. Still looking for a solution that will do the trick without harming the webbing.