  This article is a direct continuation of [1] where we begun the study of the
transfer matrix spectral problem for the cyclic representations of the
trigonometric 6-vertex reflection algebra associated to the Bazhanov-Stroganov
Lax operator. There we addressed this problem for the case where one of the
K-matrices describing the boundary conditions is triangular. In the present
article we consider the most general integrable boundary conditions, namely the
most general boundary K-matrices satisfying the reflection equation. The
spectral analysis is developed by implementing the method of Separation of
Variables (SoV). We first design a suitable gauge transformation that enable us
to put into correspondence the spectral problem for the most general boundary
conditions with another one having one boundary K-matrix in a triangular form.
In these settings the SoV resolution can be obtained along an extension of the
method described in [1]. The transfer matrix spectrum is then completely
characterized in terms of the set of solutions to a discrete system of
polynomial equations in a given class of functions and equivalently as the set
of solutions to an analogue of Baxter's T-Q functional equation. We further
describe scalar product properties of the separate states including eigenstates
of the transfer matrix.
