  We construct canonical absolute parallelisms over real-analytic manifolds
equipped with $2$-nondegenerate, hypersurface-type CR structures of arbitrary
odd dimension not less than $7$ whose Levi kernel has constant rank belonging
to a broad subclass of CR structures that we label as recoverable. For this we
develop a new approach based on a reduction to a special flag structure, called
the dynamical Legendrian contact structure, on the leaf space of the CR
structure's associated Levi foliation. This extends the results of
Porter-Zelenko [20] from the case of regular CR symbols constituting a discrete
set in the set of all CR symbols to the case of the arbitrary CR symbols for
which the original CR structure can be uniquely recovered from its
corresponding dynamical Legendrian contact structure. Our method clarifies the
relationship between the bigraded Tanaka prolongation of regular symbols
developed in Porter-Zelenko [20] and their usual Tanaka prolongation, providing
a geometric interpretation of conditions under which they are equal. Motivated
by the search for homogeneous models with given nonregular symbol, we also
describe a process of reduction from the original natural frame bundle, which
is inevitable for structures with nonregular CR symbols. We demonstrate this
reduction procedure for examples whose underlying manifolds have dimension $7$
and $9$. We show that, for any fixed rank $r>1$, in the set of all CR symbols
associated with 2-nondegenerate, hypersurface-type CR manifolds of odd
dimension greater than $4r+1$ with rank $r$ Levi kernel, the CR symbols not
associated with any homogeneous model are generic, and, for $r=1$, the same
result holds if the CR structure is pseudoconvex.
