You've gotten some good replies.
I agree with the idea of seeking the teacher's advice and input on what is working well at school. But it can be hard to apply that at home ALL the time since kids can be very different with parents than with teachers; familiarity does indeed breed contempt, as the saying goes. Plus, he wants wants wants to be the immediate center of your attention the instant your attention goes elsewhere. That's possibly a big part of this that you don't seem to see in the post - you frame it, understandably, as challenging behavior, which it is -- but I wonder if this is his way to ensure he gets attention. Remember, even the "negative attention" of your disciplining him is STILL a form of attention.
So a couple of thoughts:
Think about how much positive attention he does or doesn't get. He has two siblings and you consider him the most challenging -- is it possible that he hears his brothers getting praise or just being talked with, when the adult interactions with him tend to be more criticism? Even a child this young can pick up on unspoken feelings in parents, and if he's the kid you have to "deal with" while the others are the ones who always give you a sigh of relief -- he may be aware that he's considered a challenge. So he lives down to that.
Have you "caught him being good" lately and found things to praise, even if those things seem minor to you as the adult? You may feel you have, but to him, since the tantrums and interruptions get you 100 percent focused on him at that instant, he may feel there is more payoff in arguing for your attention than in being good for it. So when he least expects it, thank him or praise him for even tiny things he does. As adults, by the time our kids are in school, we often feel that "Well, he should just be doing/saying X by this age anyway Why lavish on the praise for what's done just to keep things going day to day?" But kids just don't see things that way.
I would absolutely see the school counselor -- you and dad, alone, without son there -- for a long talk about all this. School counselors can and do help with at-home behaviors. Explain the strong difference between his at-school and at-home selves. Ask whether your systems for reward and discipline are too complex (I don't think so, necessarily, ,but other posts here note that you have a lot of steps to your processes with him). Ask for some specific techniques to handle the interruptions. And ask about rewarding him more when he does what you ask, rather than focusing on the discipline when he doesn't. Don't leave without a list of actions you will take to change this situation on your side as well as his.
You are doing great at being consistent with discipline but I would add a warning stage before proceeding directly to removing things, and I would drop the sentence-writing; it isn't working, and he could end up associating the act of writing with punishment. (I know a kid in our school who hated the physical act of writing and said it was because his folks made him write sentences as punishment.). And I'd add a lot of "catching him being good" and giving him additional attention when he does things, anything, that is positive -- and even additional attention when it's not about his behavior but about just being with him. If your kids are all busy and it's go-go-go in your house, be sure he's getting some one on one time with you and/or dad, so he doesn't feel that he needs to act out whenever you are not focused on him.
It will take time to end his cycle of getting attention this way, possibly a lot of time. Be sure you remove your attention coldly and quickly when he does this -- overdoing the steps of lots of talking about what he did, and steps of discipline, can feed into it --that's all attention focused on him. So be short and don't over-talk each of his offenses, just warn first, discipline, then leave and don't let him have your attention for misbehaving.
I'd truly start with seeing the school counselor ASAP and finding something to praise this afternoon when he gets home from school.....