Faster-than-Nyquist (FTN) transmission employing antenna polarization multiplexing and higher order modulation (HoM) schemes can significantly increase the spectral efficiency (SE) of the existing wireless backhaul links. However, the benefits of each of these SE enhancement techniques come with a price. While FTN introduces inter-symbol interference, a dual-polarized (DP) transmission suffers from cross-polarization interference (XPI), and HoM makes a communication system vulnerable to phase-noise (PN) distortions. In this paper, we investigate, for the first time, a DP-FTN HoM transmission system. We propose a XPI cancellation and PN mitigation structure, coupled with adaptive decision-feedback equalization or linear precoding, to jointly mitigate interference and accomplish carrier-phase tracking. The DP systems combined with the FTN signaling presented in this paper offer more than 150% increase in SE compared with a single-polarized Nyquist transmission. The effectiveness of the proposed algorithms is demonstrated through computer simulations of a coded DP-FTN microwave communication system in the presence of PN. Numerical results suggest that with the proposed interference cancellation methods, a DP-FTN transmission can yield a 3-5.5-dB performance improvement over an equivalent DP-Nyquist system that employs a higher modulation order to achieve the same data rate.