Strike while the iron’s hot. Two posts in one day! Turns out I could get the desired effect by using the Reverse Warping Method. (If I do say so myself, that is an excellent tutorial.) Note that the pattern is not centered on the square. On the left border you see complete “stars;” on the right you see 2/3 stars.
Using RWM turns the pattern on its side. See the previous post for instructions on how to weave Reversible Star Boxes.