Some very good ideas here.
Press after each 'sew'.
Trim the HST's with the diagonal line on the ruler on the diagonal line of the HST.
Nest those seams when you sew one HST to another.
After pressing, nest the middle seams and put a pin here.
Start sewing at one end for a few stitches. Then lift up the top piece and see if the two are really nested the other way. There is a little wiggle room here. The top one can be moved to the right or left a smidgeon to get it right. You can see those peaks under there, and they need to be at the same level.