 Solution

A plausible extension assuming gyromagnetic ratio two iswhere the spin projection is aligned with the charge-field sign. For spin one the lowest aligned mode has $E^2=m^2{c}^4-|e|\hslash |B|c$ at $p_z=0$. Above $|eB|>m^2{c}^3/\hslash$, this is negative: linear time evolution has exponentially growing/decaying modes, signaling an instability of the assumed background.

Spin alone does not fix a magnetic moment. The scalar and Dirac examples cannot establish this formula for every higher-spin particle; the stated instability belongs to the specified $g=2$ field model and its regime of applicability. Interactions and backreaction are needed to describe its eventual outcome.