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In Part I, we defined a large class of open symplectic manifolds, calledsymplectic $\mathbb{C}^*$-manifolds, which are typically non-exact at infinity,and we showed that their Hamiltonian Floer theory is well-defined. In thispaper, we construct Morse-Bott-Floer spectral sequences for these spaces,converging to their symplectic cohomology. These are a Floer-theoretic analogueof the classical Morse-Bott spectral sequence for ordinary cohomology. Thespectral sequences determine a filtration by ideals on quantum cohomology. Wecompute a plethora of explicit examples, each highlighting various features,for Springer resolutions, ADE resolutions, and several Slodowy varieties oftype A. We also consider certain Higgs moduli spaces, for which we compare ourfiltration with the well-known $P=W$ filtration. We include a substantialappendix on Morse-Bott-Floer theory, where a large part of the technicaldifficulties are dealt with.

Symplectic $\mathbb{C}^*$-manifolds II: Morse-Bott-Floer Spectral Sequences