I think you are tilting at windmills to try to visualize spatial curvature. It really can't be completely visualized, only hinted at. If you haven't yet, check out the Wikipedia article on 3-sphere
which gets into some detail on this subject.
Keep in mind also that, unlike spacetime curvature, spatial curvature is frame-dependent. Any manifestation of spatial curvature can always be entirely eliminated by shifting the observer's velocity vector to a suitable alternative reference frame. So it is not an invariantly tangible phenomenon.
I think the most important mathematical attribute of non-flat space is that the circumference of a sphere will not measure at [tex]2\pi[/tex] times the radius. Thus when space is curved, a sphere is mathematically calculated to enclose more or less volume than would a sphere of the same radius in flat space.