  Continuing our previous work, we effectively compute connected Heegaard Floer
homologies of two families of Brieskorn spheres realized as the boundaries of
almost simple linear graphs. Using Floer theoretic invariants of Dai, Hom,
Stoffregen, and Truong, we show that these Brieskorn spheres also generate
infinite rank summands in the homology cobordism group. Our computations also
have applications to the concordance of classical knots and $0$-concordance of
$2$-knots.
