12 Angry Men.
Statler and Waldorf as the two antagonists who don’t change their votes until late. Fozzie Bear as the ad exec who changes his vote several times, except in this version he changes it every few minutes in an attempt to gain the validation of his peers.
Swedish Chef or Beaker as the naturalized citizen. Sam the Eagle as the foreman.
As for the human, that would logically be Henry Fonda, but I could also see a case being made for Joseph Sweeny instead (the old dude who changed his vote and stood up for Fonda). Kermit the Frog would play whichever of those is not a muppet.
Aso, humans (yes, plural, I know I’m cheating) could be the various minor roles like bailiff and judge, and in the spirit of other Muppet movies they would all be improbably high-profile cameos.