Previously, we demonstrated that Mg II and C IV reverberation-mapped quasars (RM QSOs) are standardizable and that the cosmological parameters inferred using the broad-line region radius-luminosity (R-L) relation are consistent with those determined from better-established cosmological probes. With more data expected from ongoing and future spectroscopic and photometric surveys, it is imperative to examine how new QSO data sets of varied quality, with their own specific luminosity and time-delay distributions, can be best used to determine more restrictive cosmological parameter constraints. In this study, we test the effect of adding 25 OzDES Mg II RM QSOs as well as 25 lower quality SDSS RM C IV QSOs, which increases the previous sample of RM QSOs by ∼36 per cent. Although cosmological parameter constraints become tighter for some cosmological models after adding these new QSOs, the new combined data sets have increased differences between R-L parameter values obtained in different cosmological models and thus a lower standardizability for the larger Mg II + C IV compilation. Different time-delay methodologies, particularly the ICCF and CREAM methods used for inferring time delays of SDSS RM QSOs, slightly affect cosmological and R-L relation parameter values, however, the effect is negligible for (smaller) compilations of robust time-delay detections. Our analysis indicates that increasing the sample size is not sufficient for tightening cosmological constraints and a quality cut is necessary to obtain a standardizable RM QSO sample.