In this study, a state-of-the-art three-dimensional (3D) drift model is used to distinguish the significant role played by particle drift in modulating galactic protons in the past two successive unusually quiet solar minima. This is done by comparing the model computations to available observations from both PAMELA and HEPD01, respectively taken in the A < 0 and A > 0 magnetic field cycles. For this abridged report, it is illustrated to what extent particle drifts occurred during the two minima. Because of these drift effects, the proton flux at lower energy is found as predicted to be even higher during the A > 0 solar minimum period of 2020 than during the A < 0 solar minimum of 2009. As such, the record of the highest ever recorded GCRs at Earth set by PAMELA has now been surpassed