Summary: We report improvements to our Sagnac effect matter-wave interferometer gyroscope. This device now has a short-term rotation-rate sensitivity of \(6\times 10^{-10}\text{ rad }s^{-1}\) over \(1 s\) of integration, which is the best publicly reported value to date. Stimulated Raman transitions are used to coherently manipulate atoms from counterpropagating thermal beams, forming two interferometers with opposite rotation phase shifts, allowing rotation to be distinguished from acceleration and laser arbitrary phase. Furthermore, electronically compensating the rotation-induced Doppler shifts of the Raman lasers allows operation at an effective zero rotation rate, improving sensitivity and facilitating sensitive lock-in detection readout techniques. Long-term stability is promising but not yet fully characterized. Potential applications include inertial navigation, geophysical studies and tests of general relativity.