Full-duplex millimeter wave (mmWave) communication has shown increasing promise for self-interference cancellation via hybrid precoding and combining. This paper proposes a novel mmWave multiple-input multiple-output (MIMO) design for configuring the analog and digital beamformers of a full-duplex transceiver. Our design is the first to holistically consider the key practical constraints of analog beamforming codebooks, a minimal number of radio frequency (RF) chains, limited channel knowledge, beam alignment, and a limited receive dynamic range. To prevent self-interference from saturating the receiver of a full-duplex device having limited dynamic range, our design addresses saturation on a per-antenna and per-RF chain basis. Numerical results evaluate our design in a variety of settings and validate the need to prevent receiver-side saturation. These results and the corresponding insights serve as useful design references for practical full-duplex mmWave transceivers.