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The trick is to simultaneously minimize the “rolling inertia” (mass moment of inertia) while also minimizing the angular velocity compared to the linear velocity. The latter is achieved by maximizing the radius that the blob rolls on, the former, by concentrating the mass as close to the c.g. (and center of rotation) of the blob as possible.
One good answer would be to take a 6cm radius sphere of low density Styrofoam (density = 0.016 g/cm^3) and hollow out just enough in the center to insert a sphere of very dense (platinum = 21.4/cm^3) metal so that the total mass is 1kg. You would have to buy and melt down a lot of platinum jewelry, but that's arguably within the rules. The approximate radius for the platinum sphere is 2.2241 cm. The overall rolling radius is maximized, while most of the mass is concentrated at the center, where it minimizes the rotational inertia. The result is a velocity at the bottom of the ramp that is 97.13% that which would be achieved if the blob was sliding-only, (the sliding-only case is the theoretical maximum). As a comparison, if the entire blob was a solid sphere of platinum (or any other material for that matter), the final rolling speed would only be 84.5% of the sliding-only speed.
However,
A better answer can be found by taking two ordinary CDs (compact discs) and gluing them as fixed wheels on the end of a steel bar (density = 7.83 g/cm^3)of the correct length for the contraption to just fit in the 12cm cube (CDs are 12cm in diameter, 0.12cm thick, with a 1.5cm center hole). To get a better result than the spheres, one would also need to drill uniformly spaced small holes in each CD, in such a way to remove half of all the material, thus halving mass of the discs, and also halving the apparent density of the polycarbonate material (density=1.2 g/cc^3). Ignoring any bits of tape or glue, the bar diameter would be 3.718cm and it would be 11.76 cm long. This blob achieves 97.38% of the sliding-only final speed. However, if one reverts to a platinum bar and starts thinning down the CDs with sandpaper or using a less dense plastic for the wheels………
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