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We derive and apply a numerical model for the description of optically injected long-cavity Fabry-P\'erot (FP) quantum-dot (QD) lasers, based on a multisection delay-algebraic-equation approach. In conjunction with experimental measurements, we characterize the multimode dynamics of the free-running laser as well as under external optical injection. We investigate the dynamics of the spatial hole burning (SHB) in the charge-carrier distribution, which is significant in QD lasers and is furthermore a driving mechanism for the emergence of multimode dynamics. In the injected laser, we focus on the transition between the locking regions of neighboring FP modes, which could not be described using traditional multimode rate-equation models. For very strong injection, the individual locking cones are found to converge. For intermediate injection strength, an additional dynamic boundary between the unlocked states is found in a narrow dynamical region in between two neighboring locking cones. This region is characterized by a further unlocking of all laser modes. Furthermore, we find the SHB to impose a threshold in the locking strength which must be overcome to lock a laser mode.