Iceblossom

If I understand the question, you are using what is sometimes called the Flynn method for making your yardage more square/wider by cutting on the diagonal and sliding down the pieces.

I would think that cutting the straight of grain inset would work fine if it was long enough. You might have to be careful sewing along the diagonal cut seam, so I would pin thoroughly.

If this was for garment construction, I'd probably advise to cut the bias so that everything would swirl nicely. You could cut it on bias like you were making continuous bias: cut Squares, divide on the diagonal, make a pennant (or I call it fangs) and sew the seam along the top.

Edit: I've really grown to like piecing backs. I do tend to use 1/2" seams and press open.