Terri, that is a beautiful quilt! There are a lot more points meeting up than I have ever seen attempted without paper piecing. Yours is way more complicated than this, but I have made some mini lone stars, so thought I might pass on what helped me get the points aligned better. I learned that it helps to use a straight pin and sink it through in the seam line of each layer at the exact place that you want the fabric pieces to meet up. Hold the straight pin steady and with the presser foot up, lower your sewing machine needle by hand into that spot. Pull out the straight pin and start your seam. Also, when you are finished matching all the points, do you know about twirling the seams where they all meet up on the back of the piece? If you use you fingers to press all the seams down and rotated like a pinwheel, then iron it like that, the center lays a lot flatter.
Hope that helps.
Jackie, your advice about doing it by hand is really great. It's funny, but I get stuck in a rut and always think I have to power through a difficult piece by machine.