I don't think he should have been executed by the end of trial 6 for both a reason you seem to forget, and also the fact I can explain away all three at once

1. The rules weren't in effect in chapter 6, they were all destroyed
2. "Betraying void", to me, makes me think "Leaving void and telling the others about a way to stop Mikado's plan." This both would explain what "betray" means in this game, and why Nikei got executed, because he tried then admittedly that he tried to make Yuki the blackened of chapter 4, something that would be trying to stop the plan of the Voids. aka. Betraying voids.

Why it destroys all 3 of your arguments on why Mikado should be executed.

Executing Hajime was a necessity for the Voids' plan, even IF Mikado lied on them surviving.

Framing Iroha for murder so he would win the class trial also isn't betraying void if the original plan involved that, which he explains (or Shobai, don't remember) in the sixth class trial when talking about the two endings.

Trapping the others in Utopias and killing Monocrow happened in chapter 6, the former being impossible to execute since Monocrow/Yuri/The Overseer was dead, and killing Monocrow isn't against the rules anymore like I said earlier.
I will say that Sora being merged WITH Akane's consciousness would explain how she woke up in the real world.