i just took a quick look and i really don't see a way to strip the entire triangle unit.
at best you could strip half the unit meaning the triangle and 1 side unit. the problem with doing this is i think you'll have tremendous waste of fabric.
draw up a mock template of what the triangle and 1 side unit would be in size. then lay out 2 pieces of paper the size the strips of fabric would be.
you'd place the seam line along the seam line of the template. then i think you might be able to flip the template and make another cut - otherwise you have to cut a straight edge and them place the template down again for the next cut.
i'll think about it some more and maybe a better way then the above will come to me.