It's a long back breaking job, but worth it in the end! A few years ago, we acquired a paddock mainly because of the stables and other outbuildings already in place, and the fact it was almost bordering some of our existing land. The paddock was a sea of yellow and from a distance resembled a rape field in full bloom!
Access with machinery is virtually impossible, but with a lot of time, patience, and sheer brute force, we cleared it over a couple of years by fencing off areas and tackling each sub-division.
Oddly enough, this morning I shifted some hay from one barn to a smaller barn at the paddock. On walking the field - which incidentally has been rested and left completely untouched for the last 12 months, I pulled out no more than half a dozen ragwort.
Tip - Dip the heads in paraffin or diesel to ensure you 'lock-in' any of the seed and prevent them being carried unburnt on the updraught from the fire. You've probably already noticed that once pulled, the flower heads wilt but they'll still go to seed if left too long before burning.
Following a burn, you could spread any resultant ash over the field with a good harrowing.
I wouldn't use Barrier H on anything other than the ragwort when in its rosette stage, i.e. any which haven't developed a flowering stalk. It will kill the mature growth but again, the flower head may still go to seed.
Next and subsequent years, target the rosettes early and for any stemmed growth, pull it preferably when the soil is damp or alternatively, dig it out using a rag fork.
Have faith and good luck