Changing a Block Pattern to a Setting Triangle

If I decide to piece this quilt on the diagonal and
if I decide to use half-square blocks like the blocks in the quilt,

then I need to know how to cut the pieces of the half-block so the edges (on the diagonal now) will be on the straight grain when finished.

I think I can leave most of the block the way it is.
I think I can cut the center square (which will be a triangle) with the straight grain along the long edge, and cut the two light squares (which will be triangles) on either end and the two red squares (which will be triangles) near the center on straight grain.

I'm just beginning to investigate this change but are there any experienced quilters who want to weigh in on this idea?  I would be ever so grateful.  Thanks in advance!

I'm linking this post to WOW at Esther's Blog and WIP Wednesday at Freshly Pieced.  Thank you, Esther and Lee.

--Nancy.
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