So, Don Momotaro, Don Dragoku, and Don Murasame.

They're the literal Don Brothers. Granted, my main points of evidence are
1. It's Inoue.
2. We've never seen or heard of Momoi's mother to my knowledge.

It's a leap, but it'd be interesting.

We don't know anything about Tarou's biological father either, since Jin only adopted him. It wouldn't surprise me if his birth name was actually Don Momotarou, which would support your theory.

Don Dragoku, real name Jiro Momoya, played by Raizo Ishikawa.

https://natalie.mu/eiga/news/479412

So he's related to the Don Momotaros?

The newest episode mentioned a "deposed Don Clan". How did I call it?

It’s very inoue to make the main lead less interesting or less relevant in screen tune than the villain or anti hero plus yellow. The rumor of new character possible 6 ranger take the place as leader remind of old day faiz system was given to Kiba for a brief time.

Why would they kill Don Momotaro off?

My guess: It's Inoue. They faked it somehow.

I mean... We know now Momoi isn't exactly human, they could easily say he's now hibernating/in a coma to regenerate or something.

As for why, remember the whole point of DonBrothers was to break free from monotonous Sentai traditions. Why not do something wild like "kill off" the red member (possibly for real) this early?

Two reasons.
1. It feels like it's just for shock value (and maybe figure sales due to the new character they need).
2. They still have Gold and Silver colors for the sixth ranger, so clearly they're not gonna break every tradition Sentai has had. (If I remember correctly, Magiranger had them turning into mechs as well.)