Further testing demonstrates that using the canonical basis as a comparison point is a fundamentally flawed idea - the principal angles of any subspace against the canonical basis are all 0 as obviously the dimensions of the subspace are orthogonal.

So classification based on characteristic vectors do not seem to be adequate to compare subspaces angles. It might be worth investigating classification methods based on an arbitrary similarity matrix, where similarity would correspond to some distance between subspaces. However, Matrix Computations only considers distance between equidimensional subspaces.