Okay, so it sounds like he’s learned that making a fuss gets him out. That’s pretty common.
I probably wouldn’t ask him to sit. That’s increasing his anticipation of release and really teaching him nothing more than to sit when asked. But I would absolutely, effective immediately, wait for him to offer up silence before letting him out, no exceptions. I would also probably go back to basics and reintroduce him to being crated, with a focus on teaching him that settling magically opens the crate door, instantaneously to start. I think KikoPup has some good videos describing this process.
You could also start by putting him in his crate as usual, then walk around the room for just a few seconds before letting him out. Increase the time slowly. You want to tell him, in poodle language, that quiet poodles get released. Then ask for a little more duration. Then a little more....
As far as the Kong goes, I would remove it after he exits to keep it a special crate treat.
It’s definitely harder to crate train a puppy that’s already developed negative associations with the crate, but I believe it can be done. Hoping others who have accomplished this will weigh in!