The concept is stupid. But on a purely craft note, if you're going to all this trouble, make the mouths close all the way, and re-do the voices to sound like the muppets.
No! Even better, get the REAL Muppet puppets (?) and the real voices actors. And re-animate Jim Henson. And stage it in the old Muppet Show (un-cancel it!). Only then will I be satisfied.