If we must have a MOTD format, then, as rgveda99 wrote, I'd like the attacks to take place inside of dreams, while the targets are asleep, where Pegasus allows the Sailor Guardians to enter dreams. This means the victims are asleep when they are targeted. However, in the name of dreams coming to life, it is the victim which is transformed into the Monster of the Day in the dream, which then transforms them in real life. Thus the only way to transform them back is to help them overcome their fears or recover their dreams.
The Amazon Trio would be under the Amazon Quartet, with the corresponding member of each overseeing their member. For instance, Jun Jun would oversee Hawks's Eye, Palla Palla would oversee Fisheye, while Ves Ves would be Tiger's Eye boss. Cere Cere, by contrast, would be doing her own thing.
I'd also have the Amazon Trio be dream demons, seemingly innocuous animals when awake with the circus as a cover, but transforming into their humanoid forms when entering the dream world. At first, they would seduce the figures in their targeted dreams, only for the dreams to turn into horrible nightmares and the victims to be under the spell of the Amazon Trio. I'd also connect the personal powerups with the targeting of the Guardian as lining up with the manga. However, this obviously leaves a hole with Cere Cere, who would target Usagi on her own. However, in that episode it is Venus who gets her powerup as she realizes her dream, not just her duty, to see the Princess happy.
I would include a special episode where MIchiru and Haruka have a falling out and are both targeted by Hawk's Eye and Fisheye respectively, only for both of them to reject the fake dreams outright (in contrast with the Inners, who do succumb). Instead of getting a powerup based on overcoming their fears, they get simultaneous powerups based on their love.
The goal of the Amazon Trio would be to take control of a dream as that is the only through the power of a dream they could truly become human. They eventually realize that it is only through their own dreams (which they do possess, in contrast with the anime) they can become human. In this way they turn against their masters and come under the protection of Helios, while it's the Amazon Quartet that do not seemingly have dreams.
However, as the Amazon Trio is reformed, the Inners wonder about the Amazon Quartet, and it is revealed their "real world" selves aren't their true selves, but distorted versions of their true dream selves as the Sailor Quartet, and they were corrupted due to fighting the nightmare queen Nehellenia who has taken their dreams.
Nehellenia is the Queen of the Dark Moon which will become Nemesis in the future, but her past is more similar to that of the manga. Her goal is to put everyone to sleep so that she can escape from the Mirror and enter reality. The conclusion would be weird, though. Nehellenia gets what she wants in that she is brought back to life in the real word by the world falling asleep, but the Sailor Guardians defeat her true self in the dream realm, which forces her to fade from reality.