Large statistical samples of quasar spectra have previously indicated possible cosmological variations in the fine-structure constant, α. A smaller sample of higher signal-to-noise ratio spectra, with dedicated calibration, would allow a detailed test of this evidence. Towards that end, we observed equatorial quasar HS 1549+1919 with three telescopes: the Very Large Telescope, Keck and, for the first time in such analyses, Subaru. By directly comparing these spectra to each other, and by 'supercalibrating' them using asteroid and iodine-cell tests, we detected and removed long-range distortions of the quasar spectra's wavelength scales which would have caused significant systematic errors in our α measurements. For each telescope we measure the relative deviation in α from the current laboratory value, ∆α/α, in 3 absorption systems at redshifts z abs = 1.143, 1.342, and 1.802. The nine measurements of ∆α/α are all consistent with zero at the 2-σ level, with 1-σ statistical (systematic) uncertainties 5.6-24 (1.8-7.0) parts per million (ppm). They are also consistent with each other at the 1-σ level, allowing us to form a combined value for each telescope and, finally, a single value for this line of sight: ∆α/α = −5.4 ± 3.3 stat ± 1.5 sys ppm, consistent with both zero and previous, large samples. We also average all Large Programme results measuring ∆α/α = −0.6±1.9 stat ±0.9 sys ppm. Our results demonstrate the robustness and reliability at the 3 ppm level afforded by supercalibration techniques and direct comparison of spectra from different telescopes.