  In this paper, we answer a question of Blecher-Muhly-Paulsen pertaining to
identifying topological invariants for completely bounded Morita equivalences
of holomorphic cross-section algebras. Given a certain natural subcontext of a
strong Morita context of $n$-homogeneous $C^*$-algebras whose spectrum $T$ is
an annulus, Blecher-Muhly-Paulsen are able to estimate the norm of a lifting of
the identity of a holomorphic subalgebra by a conformal invariant of the
annulus and a property of the associated matrix bundle. We give a
generalization of the above example in which $T$ is a bordered Riemann surface.
While constructing this generalization, we develop a sufficient criterion for
when a unital completely bounded Morita equivalence can be factored into a
similarity and a strong Morita equivalence.
