I don't think washing the #361 linen will have much effect. That stuff feels like Kevlar. It seems to be coated or impregnated with something hard.

I use my #361 a few times a week and have decent results but do tend to use the heel first.

I like the Illinois strops but prefer a softer linen too. I am about done my own series of hanging strops featuring an oil treated vegtable tanned leather and a heavy yet pliant linen, 2.5" x 24"

Tony