If you use the straight edges technique like @ShadowLucy you suggest I recommend making some small changes in the knotting structure so the black dots close to the edge stay only one knot big instead of two knots big which would happen if you just add the straight edges technique. You don't want to let the black string get to the original edge of the pattern.
Here are the changes I recommend. The numbers of the knots refer to the pattern without the added string for the straight edges technique.
Row 3: last knot fb instead of f Row 4: last knot fb instead of f Row 5: last knot bf instead of f
Row 5: first knot fb instead of f Row 6: first knot bf instead of f Row 7: first knot bf instead of f
Row 11: first knot bf instead of b Row 12: first knot bf instead of b Row 13: first knot fb instead of b
Row 13: last knot bf instead of f Row 14: last knot fb instead of f Row 15: last knot fb instead of f
If anyone is interested I could write it into a pattern using the straight edges technique.
Quick and fun to make! Tip: make both of your green strings and one red string about twice as long as the others. The red string that needs to be longer than the rest is the 4th string from the left in the pattern.