When you sew two pieces together (regardless of size) and you use a 1/4" seam allowance, you will always have to subtract 1/2" from the total. So, while 3 1/2 + 3 1/2 = 7, whe you subtract the 1/2" for seam allowance, you are left with 6 1/2.
Sometimes, when I am not sure or when I think my seam allowance may be off, I sew the pieced parts together, measure across and then cut my alternating patches to fit. You were on the right track with that idea too.