I finally got a chance to sit down with the channel for a few hours this afternoon. By happenstance, the "backgammon table" episode came up.
The only hole in my conspiracy theory here is...why would the rangefinder not moving necessitate a prize change? Unless the price got revealed for some reason, they could just replay for the original prize once they got the rangefinder moving again.
I wouldn't be surprised if, while they were pressing buttons and/or unplugging and plugging Range Game in to try to get it to work, the light behind the actual price accidentally turned on. And obviously, if they accidentally revealed the answer, they'd have to replace the prize. (Barker didn't yet have the power to declare "You automatically win!")
I agree that Bob's comments during Range Game imply that something malfunctioned the first time around. My computer froze near the end of the fourth game and I didn't get it restarted until the grocery descriptions in the fifth game, so I missed the backgammon table and Bob's comments there, but based on what you said, my money is on an accidental reveal necessitating a prize swap.
(Another bit of a hint: Later in the episode, while Bob was chatting with a contestant, he made an offhand comment along the lines of "Nothing's been going easy around here" and got a knowing laugh from Johnny.)
What was the price of the backgammon table? The living room was $2,200, so I wonder whether the table was a similar price so they wouldn't have to change the numbers on the scale itself (I didn't think to look at the board before the living room was revealed). It looked a little weird to have a living room in act one and a dining room in act three, but Bonus Game's dining room was more than $2,900.