Control of the longitudinal beam dynamics in heavy ion synchrotrons is a challenging task due primarily to the very fast time constants present in the system. Recently, the authors developed a model predictive controller for this system and demonstrated that solution of the required optimisation problem can be accomplished in about 1$\mu$s when implemented on a Field Programmable Gate Array (FPGA). This initial design made several simplifying assumptions and in this paper we extend this initial design to account for known implementation issues relevant to the SIS18 heavy ion synchrotron at the GSI Helmholtz Center. In particular, in this paper we present a design of an offset-free output feedback predictive control scheme for longitudinal beam dynamics in heavy ion synchrotrons. Furthermore, we demonstrate how to compensate for possible communication delays. The performance of this offset-free output feedback predictive controller is validated in simulation.