Herbicide; it's a bad word out in the world. It is generally frowned upon to use herbicides in gardening or farming by the general public. But . . . when you are trying your best to get control of an out of control situation, sometimes, herbicides are the answer.
Brenda and I have not used herbicides, yet on or tree farm, but we are giving it some serious consideration. We don't want to make it a part of our long term management of the forest, but we believe it has it's place in the short term to help us get our Yaupon under control.
In my search for answers, I came across a May of 2004 Master of Science Thesis titled "Managing Invasive Yaupon Holly in the Texas Post Oak Savannah" by Stephanie Dupree. Here's a link to her thesis. It's a PDF download.
Who knows, soon you may see us fighting the fight with a pack pack sprayer. Triclopyr might be the answer.