i think that bor and montgomery say that one way to think about the relationship between homogeneous distributions and graded nilpotent lie algebras is that there's some sort of "symbol algebra" of a distribution... this vaguely suggests to me the idea of taking the graded nilpotent lie algebras corresponding to bruhat cells and finding some meaningful way of "deforming them into filtered non-nilpotent lie algebras" .... or something like that.

another stray thought, maybe related: an occasional interesting source of projective varieties is projective varieties of tangent cones of singularities. does this mean that whenever you have a projective variety you should look around for a singularity of which it might be the projective variety of the tangent cone?