  In the loop quantum gravity context, there have been numerous proposals to
quantize the reduced phase space of a black hole, and develop a classical
effective description for its interior which eventually resolves the
singularity. However, little progress has been made towards understanding the
relation between such quantum/effective minisuperspace models and what would be
the spherically symmetric sector of loop quantum gravity. In particular, it is
not clear whether one can extract the phenomenological predictions obtained in
minisuperspace models, such as the singularity resolution and the spacetime
continuation beyond the singularity, based on results in full loop quantum
gravity. In this paper, we present an attempt in this direction in the context
of Kantowski-Sachs spacetime, through the proposal of two new effective
Hamiltonians for the reduced classical model. The first is derived using
Thiemann classical identities for the regularized expressions, while the second
is obtained as a first approximation of the expectation value of a Hamiltonian
operator in loop quantum gravity in a semi-classical state peaked on the
Kantowski-Sachs initial data. We then proceed with a detailed analysis of the
dynamics they generate and compare them with the Hamiltonian derived in General
Relativity and the common effective Hamiltonian proposed in earlier literature.
