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An Electro-Optic Beam Position Monitor (EO-BPM) is being developed as a high-frequency (up to 10 GHz) diagnostic for crabbing and Head-Tail intra-bunch detection at the HL-LHC. Following an earlier prototype at the SPS that demonstrated single-pickup signals, an upgraded design of an interferometric EO-BPM has been beam-tested at the HiRadMat facility for validation and characterisation studies. In the new design, the fibre-coupled Mach-Zehnder interferometer arms are modulated by lithium niobate waveguides integrated in an upgraded opto-mechanical arrangement that has been developed to produce a highly magnified image field replica of the passing Coulomb field. A new detection technique that is directly sensitive to the interferometric optical difference signal from opposite EO buttons has been applied to measure single-shot bunches for the first time. A transverse resolution study over a ±20 mm range at 3 GHz bandwidth produced the first successful electro-optic bunch-by-bunch position measurement at the HiRadMat in-air extraction line. The results of this campaign show promise for an in-vacuum design that is in production for beam tests at the SPS during Run-3 of the LHC., Proceedings of the 11th International Beam Instrumentation Conference, IBIC2022, Kraków, Poland