Canada thistles have an extensive underground root system and tillage just tends to spread the weeds by cutting the root and replanting them. Persistent mowing so as not to allow plants to seed or replenish the root system with food would have a better chance, assuming you can get to all of them with a mower. Now for chemical control, the method most of us ask about first. However, biennial thistles die easier and can be controlled with lesser rates than Canada thistle. As usual, read and follow the label.
Persistence is also key for chemical control of Canada thistle.
In general, anything Jim used with Tordon had a better rating. Stinger was a close second for control but a more costly application. I've had a plot in Page County for a couple of years using chemicals at lower rates than Jim used and have yet to be successful in controlling Canada thistles. For a copy of Jim's Canada thistle plot results, contact either me or Jim . Another counterpart of mine, Mike White , has written publications on both musk thistle control and Canada thistle control that includes excellent discussions concerning both weeds.