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Although the solution to the Micro-Gravity challenge was supplied, it is buried deep into the thread and many would not have noticed. From quite a bit of response, there were only two spot-on replies, posts #7142 and #7146 of the challenge thread. Here is the answer, as sound-boarded against a real relativist.
Ignoring surface effects (or coat all the balls in some hydrophilic substance), the lead balls end up at the top and bottom of the jar, with the plastic balls near the center. The reason is that only the center of mass (COM) of the ISS is on a perfectly natural elliptical orbit. Balls starting the experiment below the COM are traveling a bit too slow for their radial distance from Earth, so they try to go into a lower orbit. Balls starting the experiment above the COM are traveling a bit too fast for their radial distance from Earth, so they try to go into a higher orbit. The water molecules suffer the same fate, so the center of the jar ends up with a little less pressure than the top and bottom, hence buoyancy moves the plastic balls to the center.
The balls can theoretically migrate to the extremities within 20 minutes, ignoring ones that may get stuck due to surface effects. So if the crew does not use thrusters or dumps water in this period, all should be fine for the 'experiment'. Further, we can quite safely ignore mutual gravity between the balls and between balls and other objects - for more, see post #7203 of the challenge.
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relativity4engineers
