Our dog does a similar thing and if its something really good, like food he should not have, he will not back down or take substitutions. He does not care what voice or posture we use, he tries to gobble it down ASAP.
Yesterday on our walk (in the dark) he found a big turkey bone / drumstick / neck or something. He could not swallow it, but would not drop it. I had to get it away from him. Luckily he was on his leash so I walked him home, with thing in mouth. When we got inside I held him away from me with the leash and told him to drop it, my wife got the squirt bottle and I repeatedly squirted him in the face till he dropped it, which he did. As soon he dropped it, I walked him away, with no agression once he dropped it.
I did not want to do it that way, but I sure as heck was not going to grab it with my hand or hit the dog (We dont do that).
He will only do this for a food he knows he is not supposed to have & is too irrestiable. Anything else you can substitute or even take away. He draws a line in the sand for human food, which is is not allowed to have.