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A multidimensional extraction of the structure function ratio σLT′/σ0 from the hard exclusive e→p→e′nπ+ reaction above the resonance region has been performed. The study was done based on beam-spin asymmetry measurements using a 10.6 GeV incident electron beam on a liquid-hydrogen target and the CLAS12 spectrometer at Jefferson Lab. The measurements focus on the very forward regime (t/Q2 ≪ 1) with a wide kinematic range of xB in the valence regime (0.17 <xB < 0.55), and virtualities Q2 ranging from 1.5 GeV2 up to 6 GeV2. The results and their comparison to theoretical models based on Generalized Parton Distributions demonstrate the sensitivity to chiral-odd GPDs and the directly related tensor charge of the nucleon. In addition, the data is compared to an extension of a Regge formalism at high photon virtualities. It was found that the Regge model provides a better description at low Q2, while the GPD model is more appropriate at high Q2.