Yes, I agree, you will have Y seams. The only way to avoid Y seams is to cut some of the hexagons in half and sew them that way, but since your customer wants you to use t-shirts, that's probably out of the questions.
However, since you're doing a rag-style quilt, it probably won't matter much if your Y seams don't match perfectly, the rag will hide it and no one will know!