A recently proposed kinetic route to the Lorentz transform models an elementary particle as a closed lightlike intrinsic motion whose internal cycle is reallocated, under bodily translation, between intrinsic circulation and spatial advance. The construction recovers the usual time-dilation law and the Lorentz boost as a hyperbolic state map, while allowing a physical ``special'' frame in which the intrinsic tick count and the external time parameter coincide. In such a framework, ordinary closed-path clock tests are not necessarily the most sensitive probes of the special frame, because the leading directional term proportional to $Ucdotvvec$ cancels when the transported clock returns to its starting point. This paper develops a sharper null test: a one-way lifetime anisotropy measurement using unstable relativistic particles as intrinsic clocks. If a laboratory has special-frame velocity $U$ and an unstable particle beam of speed $u=beta c$ is sent along direction $$, the strong preferred-frame reading of the kinetic model predicts, to leading order,begin{equation*} tau_{m lab}() simeq gamma_u tau_0 left(1 + betafrac{Ucdot}{c}ight),end{equation*}whereas standard special relativity predicts $tau_{m lab}=gamma_utau_0$ independent of absolute orientation. Antiparallel one-way beams would therefore exhibit a fractional lifetime asymmetrybegin{equation*} frac{tau_{+}-tau_{-}}{(tau_{+}+tau_{-})/2} simeq 2betafrac{Ucdot}{c}.end{equation*}For a candidate $|U|simSI{369}{km.s^{-1}}$, as suggested by the CMB dipole scale, the maximal signal for relativistic beams is of order $2.5times 10^{-3}$, far larger than the fourth-order residuals expected in closed transport tests. The decisive experimental signature is an antiparallel lifetime or decay-length asymmetry with sidereal modulation as the Earth rotates the beam axis relative to the putative preferred-frame vector. The proposal is framed as a falsifiable extension of the kinetic model: a null result would strongly constrain the strong preferred-frame interpretation rather than merely refine an existing relativistic clock test.