The Any Light Particle Search II employs a highly sensitive heterodyne detection system to measure an ultra-weak electromagnetic field that is reconverted from axions inside a regeneration cavity (RC). The initial design of the heterodyne system utilized a local oscillator laser (LO) that was resonant with the RC to form an interference beatnote with the weak signal field exiting the cavity. A weakness of this design is that it is possible for the out-of-mode field component of the LO to be larger than the in-mode component, allowing its noise to dominate the optical component of the noise budget and reducing the SNR of the experiment. This problem can be addressed by introducing a second, non-resonant laser as the LO. Since the in-mode light of this laser does not couple to the cavity, significantly more of its power is reflected than when the LO is resonant. We present a model for the measurement noise that predicts these design changes increase the SNR by a factor of roughly 35. This model was then confirmed experimentally by injecting a weak signal to the RC and examining the difference in the sensitivity of the detection system in each of these configurations.