I decided to revisit the Balancing Robot experiment after deciding that the robot in the original video had too tall of a center of gravity. I used Technics pieces, which allowed me to use pegs to attach the motor, axles, and the distance sensor to the robot's body. I kept the gearing low and slow.
Using the Technics pieces also kept the robot lightweight, so it would not be throwing too much weight around when it ran.
After experimenting with the Scratch project, Balancing-04, I concluded that it was very capable and my previous failed efforts had been in the original robot design.
Hooking up the robot to the computer with a USB extension cable that came with a card reader gave the WeDo tether longer length. Here is the result.
As you can see, the cable plays a part in keeping the robot balanced. But the Scratch project keeps the motor running and the robot balanced quite nicely!