Embryonic development is highly robust. Morphogenetic variability between embryos (under ideal conditions) is largely quantitative. This robustness stands in contrast to in vitro embryo-like models, which, like most organoids, can display a high degree of tissue morphogenetic variability. The source of this difference is not fully understood. We use the mouse gastruloid model to study the morphogenetic progression of definitive endoderm (DE) and its divergence. We first catalog the different morphologies and characterize their statistics. We then learn predictive models for DE morphotype based on earlier expression and morphology measurements. Finally, we analyze these models to identify key drivers of morphotype variability and devise gastruloid-specific and global interventions that can lower this variability and steer morphotype choice. In the process, we identify two types of coordination lacking in the in vitro model but required for robust gut-tube formation. This approach can help improve the quality and usability of 3D embryo-like models.