I'm sorry to hear you are dealing with this! I know how frustrating it can be. Levi is kind of like Max; we always call him "the instigator." He is playful all the time and doesn't really understand that every person or dog he meets doesn't want to play with him all day long. My younger brother's dog, whom we live with, is so patient and awesome with Levi...but we've definitely come across other dogs who are more aggressive with him.
I agree with keeping them separated while they eat. My older brother has one very food-aggressive dog, so they feed all of their dogs exclusively in their crates so they are eating at the same time, but separately. I believe they get long-lasting treats (like bully sticks) only in their crates as well.
As far as the "drop it" command - I, for some reason, could not get Levi respond to the words "drop it." We switched to the word "out," and that has worked much better for us (which really doesn't make sense, as the tactics are the same). We started by trading the "dropped" item for a treat. He's also learned that when I say out, I refuse to tug on a toy/chew/item he isn't supposed to have, so it becomes less of a game to him. Once I start with the "out," he either spits it out immediately, or calms down and holds it (and apparently just waits for me to offer him a treat...crazy little monster
).
Sorry this ended up so long!!! I hope things get better! I know Cooper and Max really do love each other!