One of my listeners, Jack Powell from Quitman, Texas, wrote me that donkeys would control this big pretty weed. I like donkeys so it's definitely worth a try. Below is the best comprehensive information on the subject I have found:
Thistle Control Alternatives
What is the best way to organically control thistle and deandelion on a small plot?
Is there a low-toxicity herbicide that kills thistle as well as thistle roots?