All-solid sodium-ion batteries are a very attractive technology for large scale applications such as grid storage. Herein, a hybrid solid-state electrolyte (HybSSE) made of halloysite clay-derived Na2ZnSiO4 ceramic and ionic liquid is developed by way of high-throughput methods. This involved making over 700 ceramics in order to both optimize the synthesis and screen 22 different substituents at 8 different substitution levels. This work yielded HybSSE with ionic conductivities as high as 0.453 mS cm−1 at room temperature and 2.27 mS cm−1 at 48 °C. This is an important improvement by a factor of nearly 20 over those reported previously. The improved ionic conductivities now make this HybSSE a viable candidate for quasi-solid Na-ion batteries. Further screening of electronic conductivity shows that dendrite growth within all tested HybSSEs is not expected to be a concern, nor is electrochemical instability on the cathode side. By contrast, all HybSSEs are found to be unstable against sodium metal, with the lowest decomposition potential being 0.8 V vs. Na. Thus, sodium metal anodes are not feasible here without the use of a buffering layer. The results therefore represent important improvements in this class of electrolytes and also guide future research and development.