New theory:
The main character is the murderer. "The real Miyu in his heart" was something he wanted to get rid of, so he decided the only way to go back to normal was to kill her. He killed her during the 5:00 meeting and broke his arm in the process. Then he used the bully as an alibi. He knew the bully was struggling financially and trying to exploit people for money, so he'd be easy to control. The main character established himself as the bully's "wallet" in the months leading up to the murder so nobody would question it. The main character lied about the bully breaking his arm, which the bully assumed was just the main character trying to get him expelled or something (and was probably the last straw that made him so pissed at the MC in the present). As planned, nobody believed the bully and he was willing to grudgingly let the situation slide as long as enough money was thrown at him.
Either the main character blocked out the memory or his upbeat personality is artificial to the point where he lies in his internal monologues.