Paul-Jerry speaks truth on the Tru Oil; he and Outback Mike poured the Tru-Oil kool-aid for me, and I drank it right down; have done a few scales and brushes in it now-love it!
Jerry-I get where you are coming from on these super-stiff strops, especially some of the treated ones that are so hard you don't even want to run razors over them (at least I don't). I got a few sections of ultra-stiff fire-hose a few years ago. Steam-ironing the wrinkles out of it only swelled the fibers and made it like concrete. My solution was to put heavy duty horse-tack type hardware on it, treat one side with .5 diamond spray and the other side with CrOx crayon, and use it for knives. A few years of that and it's soft and supple as you can see in the pic.
Attachment 310813
Most will soften up with use as the fibers loosen up, though it seems like that would be a challenge with the chalk-treated ones. Personally, I like really soft linen components. I got some of that greenish linen component someone mentioned that Randy Dance was distributing. Soft as butter, it's my go-to post-shave linen, with one side treated with CrOx for touch-ups.