Used to go up there from Camp LeJune to a rock quarry 1970s. Put the canoe in at a bridge and float into the quarry-lake after lake. Don't know if I ever visited them all. Dark tea colored water and big bream. Good times!
Your enthusiasm might be a bit premature. You will have to fight to keep your new found control. Animals have scattered the berries and the will continue to pop up for years. All it takes is for you to fall behind on your control for a couple of years and the privet is off to the races again.
I use 2 oz each of triclopyr and 41% glyphosate per gallon of water applied as a foliage spray in early spring when it has just leafed out, works good for me. If its too tall to spray the foliage I mix triclopyr and kerosene 50/50 and apply from the base up 18-24 inches on the trunk. Diesel will work, but I think the kerosene works better.