With something like this I stand at the ironing board and use a straight pin pushed down exactly at the sewing line for the match (in other words, push the pin down at the 1/4" mark, making sure the pin is going through the correct point on each piece). Once I do this, I carefully lift up the seam allowance and add a tiny dot of Elmer's washable school glue to the intersection, then press with an iron to make the glue adhere. This is "glue basting" instead of pin basting. It takes a little more time to do this, but it causes less distortion than a pin does and it's less likely to shift while you sew. You could even put a dot on the non-seam allowance side of the two pieces, as after you sew it's easy to peel the pieces apart.
The only alternative I have found is to machine baste just a couple of stitches over each intersection (can do many pieces without cutting thread until after you are done), then open and check each piece before sewing the seam (which needs to go right on top of the basting thread). I find the glue basting to be easier and faster for me.
Edit: Another thing that I would try in this situation is to press the seams open. Makes the points easier to match. I also like the idea of hand sewing the points. You could hand sew just the points, then machine sew over that to sew the entire seam.