I have lots of experience.
IMO it will be a multi-year project. Yes you can get instant results with the methods above. But there will be seeds in the ground for years so be prepared to go back through with a brush killer spray when the seeds sprout the next couple years. Otherwise your efforts will be very short lived.
You can also kill mature standing buckthorn with a basil bark treatment. Mix 1 part Triclopyr 4 with 3 parts diesel gas and a blue dye. You can then spray the bottom 24 inches of live standing buckthorn and it will kill it dead.