We continue the study of Farber’s topological complexity for monotone symplectic manifolds initiated in [Or25]. First, we show that a closed spherically monotone symplectic manifold whose fundamental group contains no subgroup isomorphic to $\mathbb{Z}\oplus\mathbb{Z}$ is automatically toroidally monotone, with the same monotonicity constant. As a consequence, every closed $4$-dimensional spherically monotone symplectic manifold whose Kodaira dimension is not $-\infty$ and whose fundamental group contains no $\mathbb{Z}\oplus\mathbb{Z}$ (for instance, is Gromov hyperbolic) has maximal topological complexity $\mathrm{TC}(M)=9$. This settles, under strictly weaker hypotheses, the dichotomy $\mathrm{TC}(M)=8$, $9$ left open there. Second, we compute the topological complexity and the Lusternik–Schnirelmann category of all blowups of $S^2$-bundles over closed orientable surfaces of genus $g\geq 2$: they satisfy $\mathrm{cat}(M)=4$ and $\mathrm{TC}(M)=7$. In particular, the hypothesis on the Kodaira dimension in the first result cannot be removed, and closed symplectic $4$-manifolds realize the pairs $(\mathrm{cat}(M),\mathrm{TC}(M))=(3,5)$, $(4,7)$, $(5,9)$ in the three regimes considered in this paper. Throughout, $\mathrm{TC}$ and $\mathrm{cat}$ are taken in the unreduced convention.