I'm just catching up with your last month or so of posts. Even down here in northern Alabama, the spring is late coming. We had frost on the roofs again yesterday morning, but it's finally getting consistently warm enough to start planting here (I think)...
I really feel for you with DS 11 and school! That battle is exhausting, and it spills over into the household stuff. Or maybe it's the other way around. I don't know anymore. But I've been there with our son too. And intelligence and maturity don't always go hand in hand. With our son, the work was always too easy so like your son, he wouldn't finish everything. Classic underachiever! And oh soooo frustrating! He could spit it all out back to them on semester exams months later, and get a 97% on the test without studying even a little bit, but fail that same class because he didn't do enough "homework". In our case, throw on chronic sinus issues, sleep apnea, chronic kidney and liver issues, blood pressure problems, and fatigue, and his incentive to do homework was lower than ever. He was exhausted all the time, was throwing up most days, but knowing the material wasn't enough. His grades dropped and pretty soon he had the reputation of being stupid. It didn't take long for other kids to drop him as a friend.
One size definitely does not fit all when it comes to school. I've fought that battle for years, but you've done oh. so. much. better. at it than I have! School became a constant battleground for my son, but never in an openly defiant way. More like a quiet desperation, and a dying inside. He finally just quit trying even though he kept attending. Every teacher he's ever had felt he could have been at the top of his class. He was quiet, respectful, and always knew the answers. He often helped other kids understand the material. And by the end he started failing more classes than he was passing. (I can't even find a good emoji to express that..)
I can't even give you good advice on the school stuff.

Even looking back, I don't know what we would have or could have done differently. We didn't have the money for a more individualized school. And homeschooling just was not an option. Who knew that parenting the super smart kids would be sooo hard?? Soooo no advice, but I can say that we've been there too, and I can feel your pain and frustration.
