  We develop a framework combining the higher-twist formalism of exclusive
processes in the $s$ channel with the semi-classical effective description of
small-$x$ physics in the $t$ channel. We apply it to transversely polarized
light vector meson production, $\gamma^{*} p \rightarrow V (\rho, \varphi
,\omega) \; p$, which starts at the next-to-leading power and for which a
purely collinear treatment leads to end-point singularities. The result is
obtained in the most general kinematics, including both forward and non-forward
cases by preserving the full impact parameter dependence in the
non-perturbative correlators, in both momentum and coordinate space
representations. A systematic expansion of the Wilson lines in terms of
Reggeized gluon fields is performed in order to obtain the results in the
weak-field BFKL approximation. These new results will allow for investigating
the dilute-to-dense regime transition of QCD for a wide class of observables.
