Linen sashiko? I've honestly never seen that. All of the sashiko fabric I've seen is heavy cotton. This is the fabric and type of heavy twill that is traditionally used on these jackets:
I don't know the fabric weight exactly, but it is really high. I would guess at or over 20 oz. Does this look and sound like the fabric to which you have access?
Will need to work a bit on sourcing the fabric. Will PM you if I find something. Do let me know if you have a source. Can access it from them.