The Sagnac speed metre topology has been identified as a promising technique to reduce quantum back-action in gravitational-wave interferometers. However, imbalance of the main beamsplitter has been shown to increase the coupling of laser noise to the detection port, thus reducing the quantum noise superiority of the speed metre, compared to conventional approaches, in particular at low frequencies. In this paper, we show that by implementing a balanced homodyne readout scheme with a suitable choice of the point from which the local oscillator (LO) is derived, the excess laser noise contribution is partly compensated, and the resulting speed metre can be more sensitive than state-of-the-art position metres. This is achieved by picking-off the LO from either the reflection port of the interferometer or the anti-reflective coating surface of the main beamsplitter. We show that either approach relaxes the relative intensity noise (RIN) requirement of the input laser. For example, for a beam splitter imbalance of 0.1% in the Glasgow speed metre proof of concept experiment, the RIN requirement at frequency of 100 Hz decreases from 4 x10(-10)/root Hz to 4 x 10(-7)/root Hz, moving the RIN requirement from a value that is hard to achieve in practice, to one which is routinely obtained.