  We generalize the existing works on the way (generalized) LTB models can be
embedded into polymerized spherically symmetric models in several aspects. We
re-examine such an embedding at the classical level and show that a suitable
LTB condition can only be treated as a gauge fixing in the non-marginally bound
case, while in the marginally bound case it must be considered as an additional
first class constraint. A novel aspect of our formalism, based on the effective
equations of motion, is to derive compatible dynamics LTB conditions for
polymerized models by using holonomy and inverse triad corrections
simultaneously, whereas in earlier work these were only considered separately.
Further, our formalism allows to derive compatible LTB conditions for a vast of
class of polymerized models available in the current literature. Within this
broader class of polymerizations there are effective models contained for which
the classical LTB condition is a compatible one. Our results show that there
exist a class of effective models for which the dynamics decouples completely
along the radial direction. It turns out that this subsector is strongly linked
to the property that in the temporally gauge fixed model, the algebra of the
geometric contribution to the Hamiltonian constraint and the spatial
diffeomorphism constraint is closed. We finally apply the formalism to existing
models from the literature and compare our results to the existing ones.
