  We place the hyperbolic quantum Ruijsenaars-Schneider system with an
exponential Morse term on a lattice and diagonalize the resulting $n$-particle
model by means of multivariate continuous dual $q$-Hahn polynomials that arise
as a parameter reduction of the Macdonald-Koornwinder polynomials. This allows
to compute the $n$-particle scattering operator, to identify the bispectral
dual system, and to confirm the quantum integrability in a Hilbert space
set-up.
