M.M.
You've just described my son, who is now 8.
We finally spoke to a family therapist, when nothing we did mattered to him. He literally is not a kid that responds to ANY kind of consequences or rewards. Nothing.
The therapist made is really easy for us, and literally we made huge progress after 1 conversation. I learned that my son is a kid that needs to feel control. He needs to feel in charge of his environment. We just rearranged how we talk to him and "make requests"...and it's made ALL the difference in the world.
He chooses his punishments for certain behavior types (within reason that we've outlined), I "put him in charge" of his behavior, telling him he has the control of how things go... etc.
POOF. Totally different kid.
Maybe try something age appropriate along those lines, while you wait?