  We consider partial sum rules for the homogeneous limit of the solution of
the q-deformed Knizhnik--Zamolodchikov equation with reflecting boundaries in
the Dyck path representation. We show that these partial sums arise in a
solution of the discrete Hirota equation, and prove that they are the
generating functions of $\tau^2$-weighted punctured cyclically symmetric
transpose complement plane partitions where $\tau=-(q+q^{-1})$. In the cases of
no or minimal punctures, we prove that these generating functions coincide with
$\tau^2$-enumerations of vertically symmetric alternating sign matrices and
modifications thereof.
