It is not the job, obligation or business of our government to get involved. On top of that it is just plain stupid and dangerous. Our soldiers shouldn't be at risk for this.
Sorry to be a nit-picker, but that part of Northern Uganda/Southern Sudan is not jungle. It is semi-arid grassland, lots of big rock outcrops & boulders and very few trees. Long dry seasons and the rivers flow only during the rainy season.
As to the "Pole is Inaccessibility", there are reasonable dirt roads coming up from the south. We used to live about 100 miles east of the edge of Kony's range, in an even more inaccessible area. Back in the 1970's & 80's, our village would see a vehicle only every 6 to 18 months if we were not in there. Gulu, Kitgum and that area of Kony's territory have lots of road traffic.
From the air, I used to watch packs of wild dogs and even rabbits, let alone larger game. Put a Predator over the area at night with IR sensors and you'll spot everyone out there. There is a nice paved runway airport at Soroti, 120 miles SE of Gulu to base the Predator. Unless Kony is intermingled with the cattle herders, you would have no trouble narrowing down his location. A large group of men without cattle will either be a cattle raiding party headed to a neighboring tribe or Kony.
He could try to hide in the papyrus swamps along the White Nile north of Juba, but again IR sensors, especially at night would find him.