Beryllium metal and beryllium oxide are important nuclear materials, with neutron-induced nuclear reaction data on beryllium playing a crucial role in nuclear energy research and development. Macroscopic validation is an essential step in the nuclear data evaluation process, providing a means to assess the reliability and accuracy of such data. Critical benchmark experiments serve as the most important references for this validation. However, discrepancies have been observed in two closely related series of beryllium-reflector fast-spectrum critical benchmark experiments, HMF-058 and HMF-066, which are widely used in current nuclear data validation. A previous systematic study indicates that these two series of experiments reache contradictory conclusions in validating the neutron-induced nuclear reaction data of beryllium, creating ambiguity in improving beryllium nuclear data. As a result, the total of 14 experiments in these two series cannot currently support high-accuracy validation of nuclear data. Although most researches on nuclear data validation and adjustment mainly focus on cross sections, the angular distribution of emitted neutrons is a key factor in reactor physics calculations. In this work, we address these inconsistencies by improving the secondary angular distributions of the (n, n) and (n, 2n) reactions of beryllium, thereby making the theoretical calculations (C) and experimental results (E) of these two series more consistent, and reducing the cumulative χ² value from 7.58 using the ENDF/B-VII.1 evaluation to 4.52. All calculations based on the improved nuclear data agree with the experimental measurements within 1σ experimental uncertainty. With these enhancements, the consistency between the HMF-058 and HMF-066 series cannot be rejected within the 1σ experimental uncertainty. Based on the latest comprehensive evaluation of uranium nuclear data, this consistency is slightly improved, and the cumulative χ² value decreases to 4.36 once again. Despite these advances, systematic differences in the expected values of C/E between the two series still exist. The C/E values of the HMF-066 series are generally 230–330 pcm lower than those of the HMF-058 series, comparable to their experimental uncertainties of 200–400 pcm. Therefore, drawing a definitive conclusion about this systematic difference remains challenging. If the current improvement of differential nuclear data based on experimental data of ⁹Be is accurate, then the HMF-058 series experiments seem to be more reliable than the HMF-066 series. Ultimately, to achieve this goal, either reducing experimental uncertainty or designing and executing higher-precision integral experiments is required.