Microwave photonic phase shifters based on stimulated Brillouin scattering (SBS) offer tunable and broadband, optically controllable phase shifts. However, achieving a 360° phase shift requires a large amount of SBS gain which often exceeds the available gain and power handling capability of an integrated waveguide. A Radio Frequency (RF) interference technique has recently been utilized in an integrated silicon platform, which uses forward Brillouin scattering in a suspended waveguide to compensate for the lack of available Brillouin gain in standard silicon on insulator platforms. This interference scheme amplifies the phase shift at the expense of link performance. Here, we demonstrate and analytically model a 360° ultra-broadband phase shifter using backward SBS in both fiber and on-chip by combining SBS and RF interference. The phase enhancement scheme greatly reduces the required Brillouin gain and thus the required optical power. Additionally, the backward architecture reduces filter requirements as the residual pump reflections are simpler to remove compared to the pump in the forward Brillouin scattering case, where the pump co-propagates with the signal. The model provides a deeper insight into the properties of the interferometric phase enhancement scheme and predicts the potential trade-offs of an optimized system, showing reduced link loss at higher levels of Brillouin gain. The model also predicts the sensitivity to variations of the interferometric components. Using this technique, we have demonstrated a broadband phase shift over an ultra-broad bandwidth of 0.1 - 65 GHz, limited only by the bandwidth of the available components. Also, we demonstrate a phase enhancement factor of 10 over a bandwidth of 18 GHz in an integrated chalcogenide waveguide.