And note that of the three games cited, only one of them involves rolling out more than two set pieces (I *think* the Cliff Hangers prizes are all on a connected piece, though it's not like those or the Plinko spinners are the most challenging thing to position),
The Cliff Hangers prize stands move independently of one another, but you're right that they're easy to position.
One thing they do live to tape -- and it would be a wise move for them to show it off during a live show -- is play Plinko as the first pricing game. Drew comes out through the big doors, and as soon as the camera swings around, the big "curtain" comes down, door #1 opens up, and the stagehands get Plinko on its mark during the One Bid. They do it all without a stopdown on the regular show, and given that this special will likely have some opening remarks by Drew to buy the stagehands even more time, it would be a good choice to lead things off.
Also notable is that while all three pricing games listed have electronic components, two of them can be played even if the electronics fail. As for the other: In a pinch, a model could manually "walk" Yodely Guy up the mountain if necessary.