Current status: This is still work in progress - the current version has been slightly improved from the version in the video (I strengthened some of the elastic parts and improved the balancing). The gyro control board is my own design and currently not available yet. I will post an update once it is. The IMU is my design as well, and is available here.
The servos that will fit are the MKS DS470 (available e.g. from Hobbyking). They do have a little play, but they are very smooth and by far the fastest servo I've seen in that size and price class. I'm still on the lookout for different servos that might be a bit smoother.