So, you want to know how to effectively control Osage-orange (a.k.a., hedge).
My recommendation: during the fall or winter with a chainsaw, make a fresh stump cut or girdle on your chosen trees and then apply either Garlon 3A (triclopyr) or Pathway/Tordon (picloram) to the fresh cut. Note that these two herbicides are amine-based (water), rather than ester-based (oil). Apparently, amine-based herbicides are much more effective than ester-based herbicides in treating Osage-orange. This of course is not the case with all trees.
Pathway is ready to use (RTU), meaning no mixing is required and also comes with a blue marker dye. Garlon 3A should be applied as a 50-50 solution with water. Apply the herbicide with a spray bottle. These herbicides are effective during the dormant season.
This recommendation should get you on your way!