Why do the first executions in each game always stand out as a Cruel and Unusual Death even compared to the rest of them? Simple, it's because they're the first execution. In each game everyone is usually skeptical of Monokuma's claims at first and doubt he has as much power and brutality as he says like he does. In making the first punishment as agonizing and brutal as he can, he sets the precedence that he's every bit as scary as schoolmates planning to commit murders, and defying him just flat out isn't an option. It's also meant to shock out any hope that they have that this experience won't be unpleasant as it's made out to be, and getting caught if you decide to take the leap is going to be bad, making the future murders more elaborate and better planned.
In IF, the mastermind briefly pretends to be a Hope's Peak upperclassman named "Besshiki Madarai." In Danganronpa Zero, there's a Hope's Peak student that is an upperclassman named Isshiki Madarai who is part of a set of octuplets with 1-8 based Numerical Theme Naming (Isshiki, Nishiki, Mishiki, Yoshiki, Goshiki, Rokushiki, Shichishiki, and Yasshiki).
Junko Enoshima (the real one) has been described as Brilliant, but Lazy. While she's hardly lazy (she'd have to be quite a hard worker to go to the trouble of setting up and carrying out her scheme), it would make perfect sense if she was, as despair and laziness are both aspects of the Deadly Sin of Sloth.
Danganronpa 3 reveals that she was dependent on Mukuro for the Tragedy plans, so perhaps she was indeed a bit lazy, if brainwashing by despair anime instead of Hannibal Lecturing is any indication.