  Parametrizing TMD parton densities and fragmentation functions in ways that
consistently match their large transverse momentum behavior in standard
collinear factorization has remained notoriously difficult. We show how the
problem is solved in a recently introduced set of steps for combining
perturbative and nonperturbative transverse momentum in TMD factorization.
Called a ``bottom-up'' approach in a previous article, here we call it a
``hadron structure oriented'' (HSO) approach to emphasize its focus on
preserving a connection to the TMD parton model interpretation. We show that
the associated consistency constraints improve considerably the agreement
between parametrizations of TMD functions and their large-$k_T$ behavior, as
calculated in collinear factorization. The procedure discussed herein will be
important for guiding future extractions of TMD parton densities and
fragmentation functions and for testing TMD factorization and universality. We
illustrate the procedure with an application to semi-inclusive deep inelastic
scattering (SIDIS) structure functions at an input scale $Q_0$, and we show
that there is improved consistency between different methods of calculating at
moderate transverse momentum. We end with a discussion of plans for future
phenomenological applications.
