Any advice on getting a green Military working dog to out the Kong?

Is the Kong a reward? Perhaps switch to food? Use a second Kong to coax her into releasing the one in her mouth using the verbal command "drop" as she is releasing the kong and presenting the second kong as a reward for dropping first. Rense and repeat using variable reward schedule to enforce behavior. During my career as a dog handler, I learned that the best-trained dogs were the result of positive reinforcement.

No Offense, I am sure that many handlers will advise you, the best you can get right now is from your trainings. It is their job to ensure the Team is trained and qualified. Ask for help, it is a sign of intelligence, we all need a hand sometimes. It will also get you closer to the cadre who may be a valuable asset down the pipe.

LMAO! I didn’t read the Kong part. Have you tried the constant pressure on the choke chain while giving the command? (Avoidance Training)