There are things like thistlex (I think) and other sprays that you can use. Many people say they are harmless to anything else but I wouldn't be putting them on my land. Just my personal opinion. The 'organic' route is tougher and needs perseverance. You should wait until July when the plant has put all it's energy into producing the leaves and flowers and then top or strim before it goes to seed. This is when you can inflict maximum damage on the plant and many will die, especially if repeated year after year. Some say it's because the plant has no energy left to recover, others because the stems are hollow and fill up with water and rot. Either way, it seems to work.
I know how you feel. A field we have just taken on has been neglected for years and has a big thistle problem so I'm looking forward to a few sessions with the brush cutter next month as it's very steep. Quite satisfying work really.
The chemical route is always quicker. Just depends how you feel on that whole scene I guess. To me, it's a no go. Working with nature and using animals and our own labour should be able to solve most problems. Grass will out compete most things if given enough rest periods.