on hard core twisted braid, I just say no, or get out my 1/2" cord foot. Mending it never consistent for me either. I allow 3" total overlap, it never seems to do right with less.
butterfly :without saying how much to allow in the over all sizing ( because you know the fill pressure you want, how elastic the cloth is, and how much you sew in your seam allowance ) : ( though for the shape of them I will say this, I tend to cut 90 degree angles on corners, and I do not bow out sides for cresting ).
mark the stack of cushions all at once. Fold in quarters, lay atop one another, and clip where the pleat needs to begin to form. Or, measure each one.
Insert a pin on the wrong side, folding each pleat at 45 degrees, insert a pin just at where the line of seam would be.
Flatten pleat fullness with RS facing you. The two sides of the cushion will now appear to be a straight line in front of you. Place cushion top RS up under needle dividing half the pleat fullness ( neatly flat ) to either side of center, and inserting needle an inch back from where it would tack down this fullness.
Gently and evenly pull on the tongue as you stitch across seam line to tack down pleat fullness ( on RS ). It may be willing to pull a great deal, you need to decide how much force to apply, evenly on all corners. You could pull it out of shape if you tried, you just want to round it down some.
If this isn't what you mean by butterfly, then Dede, tell me what you mean. This is what I call a butterfly, and this makes it uniform for me. I do not try to pull the tongue and join both halves all at once. I two stage this process.
You cannot reverse grain on the halves with this and hope sides match. I get enough uniformity in my pleats where I do not have to wait and join the sides and then pleat the last set of corners. Not rounding the original cutting helps this match happen.
This isn't turkish to me, turkish is the same procedure, but gathering up the pleat fullness, and it takes a deep cushion to do it.