For the spin-LSC dynamics, we use the focused initial conditions 67 as described in section II C, where the action variable ε a is set to be 1 + Γ/2 for the initially occupied state and Γ/2 for the initially unoccupied state, with Γ expressed in Eq. 38. The angle variables {θ b } are randomly generated between [0, 2π) as in the γ-SQC method. The canonical mapping variables are obtained from Eq. 27.