  The progenitors of Type Ia supernovae (SNe Ia) are debated, particularly the
evolutionary state of the binary companion that donates mass to the exploding
carbon-oxygen white dwarf. In previous work, we presented hydrodynamic models
and optically thin radio synchrotron light-curves of SNe Ia interacting with
detached, confined shells of CSM, representing CSM shaped by novae. In this
work, we extend these light-curves to the optically thick regime, considering
both synchrotron self-absorption and free-free absorption. We obtain simple
formulae to describe the evolution of optical depth seen in the simulations,
allowing optically thick light-curves to be approximated for arbitrary shell
properties. We then demonstrate the use of this tool by interpreting published
radio data. First, we consider the non-detection of PTF11kx - an SN Ia known to
have a detached, confined shell - and find that the non-detection is consistent
with current models for its CSM, and that observations at a later time would
have been useful for this event. Secondly, we statistically analyze an ensemble
of radio non-detections for SNe Ia with no signatures of interaction, and find
that shells with masses $(10^{-4}-0.3)~M_\odot$ located $(10^{15}-10^{16})$ cm
from the progenitor are currently not well constrained by radio datasets, due
to their dim, rapidly-evolving light-curves.
