In this study we investigate the capability of the planned expansion of the Owens Valley Long Wavelength Array (OVRO-LWA) to perform radio based composition studies of the cosmic-ray flux between ~50 PeV and ~1 EeV. We use ZHAireS simulations in conjunction with a method similar to the one developed by the LOFAR experiment, but that only uses radio data between 30 and 80 MHz, to reconstruct the depth of shower maximum $X_{\mathrm{max}}$. We found that the lower antenna densities away from the central core of the array lead to a decrease in the effective area for quality $X_{\mathrm{max}}$ reconstructions of low zenith angle events, and that the asymmetry of the array layout creates the need for quality cuts that depend on arrival direction. We also investigate the dependence of $X_{\mathrm{max}}$ uncertainties on shower energy and arrival direction and show that at 500 PeV it is possible to obtain $X_{\mathrm{max}}$ uncertainties lower than 20 g/cm$^2$ for the majority of arrival directions by using a set of simple cuts. For energies below $10^{17}$ eV, alternative reconstruction methods, such as the use of hierarchical beamforming to increase SNR or the use of arrival time measurements on the ground may be needed to maintain $X_{\mathrm{max}}$ resolution at a desirable level.