The presence of excess scatter in the Ly-α forest at z ∼ 5.5, together with the existence of sporadic extended opaque Gunn-Peterson troughs, has started to provide robust evidence for a late end of hydrogen reionization. However, low data quality and systematic uncertainties complicate the use of Ly-α transmission as a precision probe of reionization’s end stages. In this paper, we assemble a sample of 67 quasar sightlines at z > 5.5 with high signal-to-noise ratios of >10 per ≤15 km s−1 spectral pixel, relying largely on the new XQR-30 quasar sample. XQR-30 is a large program on VLT/X-Shooter which obtained deep (SNR > 20 per pixel) spectra of 30 quasars at z > 5.7. We carefully account for systematics in continuum reconstruction, instrumentation, and contamination by damped Ly-α systems. We present improved measurements of the mean Ly-α transmission over 4.9 < z < 6.1. Using all known systematics in a forward modelling analysis, we find excellent agreement between the observed Ly-α transmission distributions and the homogeneous-UVB simulations Sherwood and Nyx up to z ≤ 5.2 (<1σ), and mild tension (∼2.5σ) at z = 5.3. Homogeneous UVB models are ruled out by excess Ly-α transmission scatter at z ≥ 5.4 with high confidence (>3.5σ). Our results indicate that reionization-related fluctuations, whether in the UVB, residual neutral hydrogen fraction, and/or IGM temperature, persist in the intergalactic medium until at least z = 5.3 (t = 1.1 Gyr after the big bang). This is further evidence for a late end to reionization.