We have measured beam-spin asymmetries to extract the $sinphi$ moment $A_{LU}^{sinphi}$ from the hard exclusive $vec{e} p to e^prime n pi^+$ reaction above the resonance region, for the first time with nearly full coverage from forward to backward angles in the center-of-mass. The $A_{LU}^{sinphi}$ moment has been measured up to 6.6 GeV$^{2}$ in $-t$, covering the kinematic regimes of Generalized Parton Distributions (GPD) and baryon-to-meson Transition Distribution Amplitudes (TDA) at the same time. The experimental results in very forward kinematics demonstrate the sensitivity to chiral-odd and chiral-even GPDs. In very backward kinematics where the TDA framework is applicable, we found $A_{LU}^{sinphi}$ to be negative, while a sign change was observed near 90$^circ$ in the center-of-mass. The unique results presented in this paper will provide critical constraints to establish reaction mechanisms that can help to further develop the GPD and TDA frameworks.
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