I love my digging fork! It's a favorite garden tool I use for tilling and for weed removal. Place, Stand on it , lever it back, and Pop! Also I have found that Covering areas with weed cloth or even cardboard can also cause rhizome grass root systems to grow closer to the surface for easier removal...that stuff is tenacious!
You say what you are doing is not inverting. You are by pulling up broadfork completely. You should actually open crevices only, not take broadfork action all way to point of mass soil to be uplifted, that acts in same manner of disruption as rototiller. Half way on lift would be better. Also, layer with compost after and allow to settle into crevices.
