We report a new measurement of the beam-spin asymmetry, Σ, for the reaction using quasi-free neutrons in a liquid-deuterium target. The new dataset includes data at previously unmeasured photon energy and angular ranges, thereby providing new constraints on partial wave analyses used to extract properties of the excited nucleon states. The experimental data were obtained using the CEBAF Large Acceptance Spectrometer (CLAS), housed in Hall B of the Thomas Jefferson National Accelerator Facility (JLab). The CLAS detector measured reaction products from a liquid-deuterium target produced by an energy-tagged, linearly polarised photon beam with energies in the range 1.1 to 2.3 GeV. Predictions from an isobar model indicate strong sensitivity to , , and , which corroborates results from a recent combined analysis of all KΣ channels. When our data are incorporated in the fits of partial-wave analyses, one observes significant changes in γ-n couplings of resonances which have small branching ratios to the πN channel.