Somewhere I read that the Grazon P+D claims a 76-100% root kill with a foliar treatment...
The key to that is foliar. If you shred it you will have to let it leaf back out before you spray.
Look up Grazon Next. That is what we use annually for huisatche, mesquite, and weed control.
Find the local contractors in that area with the buggies to fertilize and spray. They should know what kills them. There are probably others in that area who fight them also.