We report on Hall field-induced resistance oscillations (HIROs) in a 60-nm-wide GaAs/AlGaAs quantum well with an in situ grown back gate, which allows tuning the carrier density n. At low n, when all electrons are confined to the lowest subband (SB1), the HIRO frequency, proportional to the product of the cyclotron diameter and the Hall field, scales with n(-1/2) as expected. Remarkably, the population of the second subband (SB2) significantly enhances the HIROs, whereas their frequency now scales as n(-1). We demonstrate that in this two-subband regime HIROs still originate solely from backscattering of SB1 electrons. The unusual density dependence occurs because the population of SB2 steadily increases, whereas that of SB1 remains essentially unchanged. The enhancement of the HIROs manifests an unexpected steplike increase in the quantum lifetime of SB1 electrons, which reaches a record value of 52 ps in the two-subband regime.