  In this paper we continue the study in [Gilton-Levine-Stejskalova] of
compactness and incompactness principles at double successors, focusing here on
the case of double successors of singulars of countable cofinality. We obtain
models which satisfy the tree property and club stationary reflection at these
double successors. Moreover, we can additionally obtain either approachability
or its failure. We also show how to obtain our results on $\aleph_{\omega+2}$
by incorporating collapses; particularly relevant for these circumstances is a
new indestructibility theorem of ours showing that posets satisfying certain
linked assumptions preserve club stationary reflection.
