Lanajoyce, I understand your question. This sweet little basket has been a bit of challenge. I just now cut striped fabric to test the directions and you are correct--those stripes do not all run North/South as you would like with a strong directional print. The only thing I can suggest is to cut the squares in half on the diagonal, but do not sew them into a HST. Cut again so you get ONE triangle going North/South, and repeat with another directional square--this will create triangles you won't use but allows you to get the stripes in the correct orientation. Once you are happy with the directions the triangles are going, sew them together. The unused triangles are leftovers.
I don't know of any other way you could cut the striped fabric to get them all going North/South. If you were willing to have one block go East/West, that would work but you would have to cut the A rectangle going East/West too.
I hope this puts your mind at ease. You are not doing anything wrong.