Once an area is heavily infested, it's a big job to get rid of Buckthorn. I battled it for years on my own property and came to the realization that it was spreading faster than I was making headway against it. I applied for an EQIP grant through NRCS that paid for about 75% of the cost of hiring a contractor to deal with it. The first grant paid for about 25 acres, about 2/3 of which was heavily infested, the rest moderate. We just finished up a 2nd grant covering a similar area. This second grant also covered some other wildlife habitat improvement practices, which I am doing myself - getting paid for, which helps cover my portion of the cost of the invasive work.

When I was working on my own, I started out trying to deal with it solely by mechanical means (repeated cutting). That proved to be very labor intensive, with many plants needing to be cut back multiple times. I switched to cut stump treatment: cut the Buckthorn, then treat the stump by "painting" or dabbing on glyphosate (Roundup). If I recall, I used 25-30% concentration (the stuff at the local hardware store was only a few % concentration, and totally ineffective at preventing the stump from resprouting).  NOTE: if you are doing a lot of this sort of work a brush cutting saw or clearing saw (like a weed whacker on steroids, with "bicycle" style handle bars and what almost looks like a circular saw blade on the end) is a LOT easier to use than a chainsaw. You just need to be sure you get a unit large enough to handle this sort of blade.

I have found Triclopyr to be very effective for cut stump treatment. You don't need a license to buy it. It works better for me than Roundup.