  This is an ultimate completion of our earlier paper [Acta.\ Math.\ Hungar.\
140 (2013), 248--292] where mapping properties of several fundamental harmonic
analysis operators in the setting of symmetrized Jacobi trigonometric
expansions were investigated under certain restrictions on the underlying
parameters of type. In the present article we take advantage of very recent
results due to Nowak, Sj\"ogren and Szarek to fully release those restrictions,
and also to provide shorter and more transparent proofs of the previous
restricted results. Moreover, we also study mapping properties of analogous
operators in the parallel context of symmetrized Jacobi function expansions.
Furthermore, as a consequence of our main results we conclude some new results
related to the classical non-symmetrized Jacobi polynomial and function
expansions.
