Binaural reproduction of high-quality spatial sound has gained considerable interest with the recent technology developments in virtual and augmented reality. The reproduction of binaural signals in the Spherical-Harmonics (SH) domain using Ambisonics is now a well-established methodology, with flexible binaural processing realized using SH representations of the sound-field and the Head-Related Transfer Function (HRTF). However, in most practical cases, the binaural reproduction is order-limited, which introduces truncation errors that have a detrimental effect on the perception of the reproduced signals, mainly due to the truncation of the HRTF. Recently, it has been shown that manipulating the HRTF phase component, by ear-alignment, significantly reduces its effective SH order while preserving its phase information, which may be beneficial for alleviating the above detrimental effect. Incorporating the ear-aligned HRTF into the binaural reproduction process has been suggested by using Bilateral Ambisonics, which is an Ambisonics representation of the sound-field formulated at the two ears. While this method imposes challenges on acquiring the sound-field, and specifically, on applying head-rotations, it leads to a significant reduction in errors caused by the limited-order reproduction, which yields a substantial improvement in the perceived binaural reproduction quality even with first order SH.