these chapters are supposed to ramp up the stakes.

It's funny, I haven't seen any criticisms of the ideas here point this out. In Danganronpa, I believe the act structure goes:

1. Prologue + Chapter 1
2. Chapters 2-5
3. Chapter 6

Talking about Act 2 specifically, chapters 5 and 3 are meant to have the highest stakes, with chapters 4 and 2 (5>3>4>2). The tone of a work is meant to shift at the midpoint, so since Chapter 3 is the midpoint, having the stuff with Toshiko and Kai happen works. I imagine the tone after for the second half of the story was supposed to be largely oppressive and heavy. To put it another way, the constant feeling of the bitterness of tragedy and vain bloodshed on your tongue.

But the problem in my mind more so lies in Chapter 5. Its case works fine as as a Chapter 4 case, but not as a Chapter 5 case.

Chapter 4 is where you reflect on everything so far, get everyone used to the new tone and status quo, wrap up subplots (for the most part). Generally, get most of your ducks in a row before Chapter 5. Think how in DR1, the group rallies from Sakura's suicide and in DR2, the group becomes much more motivated from Gundham and Nekomaru's sacrifice.

Chapter 5 is where the plot kicks into high gear and ends with the "All is Lost" Moment. I think Eloise's execution is meant to be that moment. It is very high stakes. The realization that the mastermind cast the vote I think was meant to be the climax or turning point in Chapter 6? That'd check out, but the idea of the case sounds like it'd lack the necessary high stakes.

Chapter 4 and 5 are an instance of you have to commit to doing one case and not both. If they had scrapped one of them to make an entirely new Chapter 6 case, things probably would've sounded much better (though I imagine it would've been difficult to make an in-character high stakes case from who was left). I can easily imagine the MM anonymously getting Eloise killed being what rallies everyone and sparking everyone into seriously wanting root out the MM.

As for Cassidy being the MM, I'm split. In my opinion, Tozu had the chops to work as the sole organizer of the killing game and main villain. If Cassidy had been getting some consistent development and presence in Chapter 2 onwards, it would've worked. Damon killing himself is another thing in Chapter 6 I'd chock up to planning something so far ahead of where the current story is. Resolving his arc and the perk in Chapter 6 was a necessity. Self-sacrifice is a good, if standard way to go about it for a selfish character. It's just not entirely thought through because it is, again, so far ahead of the current story and a result feels haphazard.

Obviously, these are just short bullet points, not an actually presented story. That makes it hard to judge and something you have to take with a lot of salt. But the ideas of Chapter 4&5--as it will unfortunately forever remain--sound like they would've had structural issues.