Hi OP!
From what I am gathering here you are seeking a way to motivate your team to do their job. You have implemented the standard best practices to clarify to each worker his/her duties and streamlined kitchen tasks with little success. Do I have that right?
So let’s step back and get a birds-eye view of your staff.
From your original post we have people with:
-Lower kitchen line skill sets
-Entitled Attitudes
-No enthusiasm for food
-Unmotivated to do better
-Restrictive (PC)/low on humor???
So the root of the problem appears to be that your team isn’t “buying in” to working as a team and making the kitchen a successful, well oiled machine.
So let’s put our heads together and see what can be done to improve things.
First off, what are your insights as to why they are in this job? Benefits? The only gig they could land? Job security?
-what would it take to get their cooking skills up to par? Could corporate pay for something like
https://rouxbe.com/industry-training/?
-Buy in....hmm okay so we know that humans want to feel loved and accepted, valuable and have purpose. So how do we foster this in the context of the kitchen....have you heard of Donald Miller’s storyline?
https://podcasts.apple.com/us/podcast/building-a-storybrand-with-donald-miller/id1092751338
So his audience is copyeditors, but his message relates here. So a basic story is you have a hero, hero meets a guide who calls them to action and hero either succeeds or fails. His principles for advertising actually work quite well for your problems.
So I want you to close your eyes and visualize this: Your workers are a bunch of Luke Skywalkers, (feckless teenage ne'er do wells), and maybe a hans solo and Chewbacca thrown in the mix. You are Yoda/Obiwan Kenobi leading your heros to success. The kitchen is the the Sith. We have to rebalance the Force.
Okay now that we have reframed the problem, how do we call the hero’s to action? It’s probably gonna have to be twofold. Working individually to see what each person is motivated by and what they want at work, maybe even what they find “painful” enough as a consequence for bad choices to stop bad behavior. Then the addressing the team as a whole in some motivating way and maybe implementing some new structure?
Sorry I am still chewing on this and developing ideas as I go. Is anything ringing true for you? Am I getting close to the answer you were seeking?
If none of this is helpful maybe try another forum like Reddit? The have a subreddit for chefs, management, entrepreneurs lots of different industry cross-sections someone might be more helpful there.