Nagato has to actually know an attack is coming to use Preta, that's why he didn't just have Preta activated to absorb Itachi's Amaterasu Flames, becuase he didn't know the attack was coming as he thought Itachi was on his team. Nagato won't know an attack is coming if the Clam's Genjutsu is in place and he'd also struggle w/ a Mu invis attack for the same reason. Also there are plenty of physical attacks the Gokage are capable of that can end Nagato. Such as Mu slicing his head off w/ a sword or Sandaime Raikage beating him to a pulp w/ his immense physical strength. Finally Preta realm does not work on things like Gaara's Sand, we saw that here:
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Maddy: sand added to water....
Gaara: not just sand!
May in her mind: if you don't like the sand you can stop absorbing jutsu, you know.
well...then you will be too electrified with raisuiryudan(=electric water dragon shot/bomb) to move
So Yondaime Kazekage's Gold Dust should also work fine against Nagato. There are plenty of options to get around Preta realm's ability.
The Genjutsu is Cast by the Clam, not the Mizukage. The fact that the Clam can also cloak the position and generate Mirages of the Mizukage, already demonstrates that it can be utilized on teammates, since Mizukage is the Clam's teammate.
I can't imagine that Mu w/ his strongest Jinton + Sandaime's Black Lighting + Joki Boi + Gold Dust Attack, can't bust CT's core.