This is a very interesting mechanic, though as you say - 100d6 is a hell of a lot to manage!
I've been given another suggestion via Chris Sims on Twitter that I wanted to share, along with one of my own. Chris' is:
Start with 9 tokens. When instructed to pull from the tower, instead roll the die. If the die shows 6, you lose one token. If your number of tokens falls to between 5 and 2, you lose a token if the die shows the number of tokens you have left or a higher number. When you have one token left, you still need to roll a 2 or higher to lose a token. So, for instance, if you have one or two tokens left, a roll of 2 or higher causes you to lose one token. When you lose your last token, the “tower” falls.
That led me to what may be a simpler mechanic. Start with a counter that you set to 30 (the average number of pulls in a Jenga game - but you could set this to anything you like). When you're instructed to pull from the tower, reduce the counter by 1 and roll a d6. If you roll equal to or higher than the counter number, the tower falls.
Realistically you don't start rolling until the counter hits 6, obviously.
Keep the ideas coming!