  A recent solution of the hyperon puzzle by a first order phase transition to
color superconducting quark matter is revisited in order to replace the Maxwell
construction by an interpolation method which describes a mixed phase. To do
this, we apply for the first time the finite-range polynomial interpolation
method for constructing a transition between hadronic and quark matter phases
to the situation that is characterized in the literature as the reconfinement
problem. For the description of the hadronic phase the lowest order constrained
variational method is used while for the quark phase the nonlocal
Nambu-Jona-Lasinio model with constant (model nlNJLA) and with
density-dependent (model nlNJLB) parameters is employed. Applying the
replacement interpolation method to both quark matter models results in a
hybrid equation of state that allows a coexistence of nuclear matter,
hypernuclear matter and quark matter in a mixed phase between the pure hadronic
and quark phases which can also be realized in the structure of the
corresponding hybrid star sequences. The predicted hybrid stars fulfill the
constraints on the mass-radius relation for neutron stars obtained from recent
observations.
