The objective of this study was to improve the precision of linear energy transfer (LET) measurements using Al₂O₃:C optically stimulated luminescence detectors (OSLDs) in proton beams, and, with that, improve OSL dosimetry by correcting the readout for the LET-dependent ionization quenching. The OSLDs were irradiated in spot-scanning proton beams at different doses for fluence-averaged LET values in the (0.4-6.5) keVμm^-1 range (in water). A commercial automated OSL reader with a built-in beta source was used for the readouts, which enabled a reference irradiation and readout of each OSLD to establish individual corrections. Pulsed OSL was used to separately measure the blue (F-center) and UV (F⁺-center) emission bands of Al₂O₃:C and the ratio between them (UV/blue signal) was used for the LET measurements. The average deviation between the simulated and measured LET values along the central beam axis amounts to 5.5% if both the dose and LET are varied, but the average deviation is reduced to 3.5% if the OSLDs are irradiated with the same doses. With the measurement procedure and automated equipment used here, the variation in the signals used for LET estimates and quenching-corrections is reduced from 0.9 to 0.6%. The quenching-corrected OSLD doses are in agreement with ionization chamber measurements within the uncertainties. The automated OSLD corrections are demonstrated to improve the LET estimates and the ionization quenching-corrections in proton dosimetry for a clinically relevant energy range up to 230 MeV. It is also for the first time demonstrated how the LET can be estimated for different doses.