Paper piecing might help you.
One thing that I found is that I found is that how you approach cross seams matters a lot, as does pinning. First put a pin vertically right next to the cross seam, through both pieces. This is the standard procedure. Holding it carefully, pin on either side of the first pin. (although, I generally use one pin on a diagonal.) Look at our left hand example. If you were sewing from bottom to top, It would be positioned correctly, so that your needle hits the seam allowance and locks it in place before it reaches the cross seam. If you have the reverse, the cross seams tends to be pushed apart. Of course, you may say, "What about pressing to the dark?" Where that is a problem, I clip the seam once so it can be pressed to the dark.
When a large number of people in my guild were working on a project together, I found that several people who had been quilting much longer that I had this exact problem and had convinced themselves that they did not care. After one try with this method, they were comfortable with being "experts". Don't give up.
Do get new blades. Rotary cutting is much faster and more exact.