I've been fighting my infestation of canada thistle for the past 30 years. Did you know, the average infestation has a root system 10 miles long? As was pointed out in an earlier post, the root system is quite deep, and runs vertically, and horizontally in several directions.
I have mistakenly rototilled, (bad idea), mowed, pulled, and sprayed. Decapitation, below the surface, and spraying in the fall when the plant is pulling energy into the roots works well. I haven't used any herbiced other than glyphosate, and on occasion, Crossbow mixed with glyphosate.
There is mechanical means of control. Having a good idea of the root depth of my infestation, I started at the perimeter, and using my loader mounted forks, I used them as spears. I make sure I am at least a couple of feet away from the crown of the plant. I pry up, and take a large chunk of soil, (mine is heavy clay), and flip it onto the ground.
Once you've done this, it is very important to heavily sow some deep diving cover crops, and some grasses. This will help choke out the offending thistle.
Then I carefully extract every single piece of root I can find. This forks have proven to be a tremendous tool in my fight against this horrible plant.
I have also gained the victory of a 5 acre infestation of yellow star thistle, and smaller outbreaks, but even worse, of the dreaded goat heads.
When it comes to noxious weeds, my motto: When you think you've gotten them all, think again. You must be in relentless pursuit it you want to maintain the value of your property.