I found your research after listening a Quiz at the TV and was curious to undertsand.
Then I went to see the video for your research.
I believe there is a major mistake in your work.
If I correctly understood, you suspended the human to reduce the weight down to the equivalent of the Moon surface weight.
Then your "tester" run quickly the legs to create a "lifting" force to walk onto the water.
The mistake, on my point of view, is that you didn't reduce the water "weight" and, therefore, the available reaction force was much higher that on the moon.
As per the Archimede principle, A body immersed in a liquid, receives a push upward equal to the weight of the volume of the removed liquid. Therefore, when on the moon, a body weights about 1/6 that on the Earth but also the water weights 1/6. The volume remaing the same, the push will be 1/6 that on the Earth.
Then the immersed volume will be the same as with force exercised while "walking" on the water on the Moon.

I'll searchfor the equations you refer in the article but I'm quite sure the will some evidence of the whater specifi gravity or density and gravity acceleration.
I hope my explanationis clear enough to be understood. Pardon my poor English.