Not that I have any personal experience in this specific situation....so please understand I am just thinking out loud here
Sometimes I have heard that it helps to have all of the chores and expectations established and written out in some contractual agreement. Certainly they teach you in education classes that the classroom rules should be clearly established and that the consequences are outlined. Can't imagine a home situation is too different.
Maybe this could help. I mean, in his rational mometns, you guys could sit down with him, pray with him, and explain to him the expectations. When he comes home from school, he needs to...., If he do not, then this will be what happens.....No arguments, no negotiations, no discussion.....did not help with setting the table, no TV. No argument, no discussion. You could write this up and create a contract that becomes an easy reference....
I know from teaching that sometimes you can also have them participate in the discussion. He must do some chores when he gets home. Is there a list of four or five that he could then choose two or three to get done? This might allow him to feel part of the decisions. But you have established that you and your wife are the ones who will mete out the consequence. And there could be one or two that are non-negotiable.
In the emotional moments, it is tempting to engage in the debate, as if you should be able to argue him to your side. But there really does not need to be any debate, especially in the emotioanl times. At that point, all you have to say is "No discussion... consequence" "This is non-negotioable" ESPECIALLY in the emotional, irrational moments. (I spent a frustrating couple of years as a beginning teacher thinking that I must win every argument, disciplining became a lot easier when I simply would look at the student and say....no discussion....you broke the rule....here's the conseuence. ) and tyo be honest....it becomes a bit of a relief to the students....you are calm, you are not reacting in *response* to their emotion but simply following the rules. That very "impersonal" reaction allows me to then get back to being a teacher. "Yeah, you were late....this is the third tardy to class....here's the detention....no discussion....let's get back to class..." and then you can give them attention in the class that's appropriate attention.
On the flip side....is he tired after school, could he benefit from some sort of palnned downtime? quiet time? Could this be a moment that he and your wife could share a snack and "vent" together? I remember fondly coming home from school and having a snack with my mom while I briefed her on the day. Then it was on to homework

Some days this meant crying, some days just being tired at the kitchen table. Maybe this could be a prayer time? Just brainstroming here....
And this might be a silly question....but does he get recess at school? Could he be frustrated with energy? I am constantly amazed at the energy the boys at school have....I think they could play ALL day long. They play before school, they play at lunchtime, and they play in gym, and they play after school....(youth is wasted on the young

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NOT THAT THIS EXCUSES INSOLENCE OR RUDENESS, but just thinking of simple reasons for frustration....
Does he give you any reasons for afternoons as being particularly frustrating?