This study demonstrates that using spin-polarized deuterium-tritium (D-T) fuel with more deuterium than tritium can increase tritium burn efficiency (TBE) by at least an order of magnitude without compromising fusion power output, compared to unpolarized fuel. Although previous studies show that a low tritium fraction can enhance TBE, this strategy resulted in reduced fusion power density. The surprising improvement in TBE at fixed power reported here is due to the TBE increasing nonlinearly with decreasing tritium fraction but the fusion power density increasing roughly linearly with D-T cross section. A study is performed for an ARC-like tokamak producing 481 MW of fusion power with unpolarized 53:47 D-T fuel, finding the minimum startup tritium inventory ($I_{\mathrm{startup,min}}$) is 0.69 kg. By spin-polarizing half of the fuel and using a 60:40 D-T mix, $I_{\mathrm{startup,min}}$ is reduced to 0.08 kg, and fully spin-polarizing the fuel with a 63:37 D-T mix further reduces $I_{\mathrm{startup,min}}$ to 0.03 kg. Some ARC-like scenarios {are predicted to} achieve plasma ignition with relatively modest spin polarization. These findings indicate that, with advancements in helium divertor pumping efficiency, TBE values of approximately 10-40\% could be achieved using low-tritium-fraction and spin-polarized fuel with minimal power loss. This would dramatically lower tritium startup inventory requirements and reduce the amount of on-site tritium. More generally than just for spin-polarized fuels, {increased} plasma performance can be used to increase TBE. This strongly motivates the development of spin-polarized fuels and low-tritium-fraction operation for burning plasmas.