A key goal of synthetic morphogenesis is the identification and implementation of methods to control morphogenesis. One line of research is the use of synthetic genetic circuits guiding the self-organization of cell ensembles. This approach has led to several recent successes, including control of cellular rearrangements in 3D via control of cell-cell adhesion by user-designed artificial genetic circuits. However, the methods employed to reach such achievements can still be optimized along three lines: identification of circuits happens by hand, 3D structures are spherical, and effectors are limited to cell-cell adhesion. Here we show the identification, in a computational framework, of genetic circuits for volumetric axial elongation via control of proliferation, tissue fluidity, and cell-cell signaling. We then seek to implement this design in mammalian cell aggregates in vitro. We start by identifying effectors to control tissue growth and fluidity in vitro. We then combine these new modules to construct complete circuits that control cell behaviors of interest in space and time, resulting in measurable tissue deformation along an axis that depends on the engineered signaling modules. Finally, we contextualize in vitro and in silico implementations within a unified morphospace to suggest further elaboration of this initial family of circuits towards more robust programmed axial elongation. These results and integrated in vitro/in silico pipeline demonstrate a promising method for designing, screening, and implementing synthetic genetic circuits of morphogenesis, opening the way to the programming of various user-defined tissue shapes.