I think publius has a better handle on the whole state of these affairs but in his absence I will state that length contraction is always a single axis/dimensional phenomenon.

In Special Relativity the length contraction is in the direction of travel which if the travel is along the X-axis then all the length contraction will be evident along the X-axis.

For gravity the length contraction is along the radial vector away from the center of gravity.

So in both cases the length contraction is only evident in one dimension whether this phenomenon actually causes a "density" change, since volume would be affected by length contraction, could be debated.