Kill more sows, shoats and even pigglets, not just boars.A sow can have 2 or 3 litters a year even more in states like FL.. You have to kill every pig you see anytime you see one.. And the truth be known it's going to be hard to eliminate them totally by just shooting them..
Are you using large corral traps that will hold several hogs or just a big box trap, even trap shy old boars can be lured into a corral trap , it might take a weeks of feeding/ baiting to get them used to the corral.

Here in GA they are pretty bad and spreading, we can hunt them year round on private land we can bait them and even shoot them at night..

I agree with everything you said except the "even more". 3 litters per year is max. It takes 3 month, 3 weeks, 3days, from the time of mating to birth of the litter. 3 litters per year is the max. Now rabbits........... :s4: