Movement with moon physics (such as in Space Zone 1), space physics (such as in Space Zone 2), and the bubble (such as in the Hippo level) are all identical, with the rather obvious exception that you can float indefinitely with space physics and the bubble.
This leads me to believe there was some confusion about the potential speeds, though the faster speed was used in both this TAS and the previously published TAS.
The oscillation patterns (which can be seen at memory address A200) are 8 frames long and vary.
Mario's speed (which can be seen at memory address A202), at top speed, oscillates between 1 and 2. I'll attempt to explain both based on my experience. There is also a 'better' pixel trick, which is even faster, but was not used in the previously published TAS (or my cancelled TAS) because it is restrictive. As described in the published TAS, the pixel trick allows for faster movement than humanly possible, thanks to frame-by-frame control.