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Several recent works have focused on the search for bright, high-z quasars (QSOs) in the South. Among them, the QUasars as BRIght beacons for Cosmology in the Southern hemisphere (QUBRICS) survey has now delivered hundreds of new spectroscopically confirmed QSOs selected by means of machine learning algorithms. Building upon the results obtained by introducing the probabilistic random forest (PRF) for the QUBRICS selection, we explore in this work the feasibility of training the algorithm on synthetic data to improve the completeness in the higher redshift bins. We also compare the performances of the algorithm if colours are used as primary features instead of magnitudes. We generate synthetic data based on a composite QSO spectral energy distribution. We first train the PRF to identify QSOs among stars and galaxies, then separate high-z quasar from low-z contaminants. We apply the algorithm on an updated dataset, based on SkyMapper DR3, combined with Gaia eDR3, 2MASS and WISE magnitudes. We find that employing colours as features slightly improves the results with respect to the algorithm trained on magnitude data. Adding synthetic data to the training set provides significantly better results with respect to the PRF trained only on spectroscopically confirmed QSOs. We estimate, on a testing dataset, a completeness of ~86% and a contamination of ~36%. Finally, 207 PRF-selected candidates were observed: 149/207 turned out to be genuine QSOs with z > 2.5, 41 with z < 2.5, 3 galaxies and 14 stars. The result confirms the ability of the PRF to select high-z quasars in large datasets.