I don't like the tube method either.
I fold my squared off end over to the selvedge. I do this on my big cutting table with a 4'x8' mat. You can always fold down to fit your mat.
I use my longest, heaviest ruler to cut the strips.
I now have a piece of plexiglas with a strip of emery cloth 1/2" wide glued down the center to hold it in place.
I wish they made emery cloth in different widths like a roll of tape. And while I'm wishing, I want it to be transparent.