  This paper is a continuation of [1], in which a set of matrix elements of
local operators was computed for the XXZ spin-1/2 open chain with a particular
case of unparallel boundary fields. Here, we extend these results to the more
general case in which both fields are non-longitudinal and related by one
constraint, allowing for a partial description of the spectrum by usual Bethe
equations. More precisely, the complete spectrum and eigenstates can be
characterized within the Separation of Variables (SoV) framework. One uses here
the fact that, under the constraint, a part of this SoV spectrum can be
described via solutions of a usual, homogeneous, TQ-equation, with
corresponding transfer matrix eigenstates coinciding with generalized Bethe
states. We explain how to generically compute the action of a basis of local
operators on such kind of states, and this under the most general boundary
condition on the last site of the chain. As a result, we can compute the matrix
elements of some of these basis elements in any eigenstate described by the
homogenous TQ-equation. Assuming, following a conjecture of Nepomechie and
Ravanini, that the ground state itself can be described in this framework, we
obtain multiple integral representations for these matrix elements in the
half-infinite chain limit, generalizing those previously obtained in the case
of longitudinal boundary fields and in the case of the special boundary
conditions considered in [1].
