Due to their unique combination of features such as large deformation, high compliance, lightweight, energy efficiency, and scalability, dielectric elastomer (DE) transducers appear as highly promising for many application fields, such as soft robotics, wearables, as well as micro electro-mechanical systems (MEMS). To generate a stroke, a membrane DE actuator (DEA) must be coupled with a mechanical biasing system. It is well known that nonlinear elements, such as negative-rate biasing springs (NBS), permit a remarkable increase in the DEA stroke in comparison to standard linear springs. Common types of NBS, however, are generally manufactured with rigid components (e.g., steel beams, permanent magnets), thus they appear as unsuitable for the development of compliant actuators for soft robots and wearables. At the same time, rigid NBSs are hard to miniaturize and integrate in DE-based MEMS devices. This work presents a novel type of soft DEA system, in which a large stroke is obtained by using a fully polymeric dome as the NBS element. More specifically, in this paper we propose a model-based design procedure for high-performance DEAs, in which the stroke is maximized by properly optimizing the geometry of the biasing dome. First, a finite element model of the biasing system is introduced, describing how the geometric parameters of the dome affect its mechanical response. After conducting experimental calibration and validation, the model is used to develop a numerical design algorithm which finds the optimal dome geometry for a given DE membrane characteristics. Based on the optimized dome design, a soft DEA prototype is finally assembled and experimentally tested.