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We present an improved technique for estimating a muon's energy by measuring the deflections along its path inside the MicroBooNE detector from multiple Coulomb scattering (MCS). This approach implements several innovations that better capture detector non-idealizations compared to previous MCS-based muon energy estimators. As a result, it achieves improved resolution, reduced bias, and better data-model agreement. Using model simulation, for fully contained events the estimated bias is within 1% and the estimated resolution varies from 4.3% to 10% as muon energy increases from 0.1 GeV to 2 GeV. For events with particles exiting the detector volume, at least a meter of reconstructed muon track, and a muon energy below 2 GeV, the estimated bias is less than 2% and the estimated resolution varies from 7% to 17% over muon energy. These demonstrate significant improvements over the performance of previous work using an MCS-based energy estimator at MicroBooNE, which achieves twice as large a resolution as well as a bias of 20% over the same energy region. Data-model goodness-of-fit studies are used to validate the estimator's performance on data, showing good agreement within model uncertainties.