Scaling trends of reconfigurable hardware (RH) and their design flexibility have proliferated their use in dependability-critical embedded applications. Although their reconfigurability can enable significant fault tolerance, due to the complexity of execution time in their design flow, in-field reconfigurability can be infeasible and thus limit such potential. This need is addressed by developing a graph and set theoretic approach, named hypergraph-cover diversity (HCD), as a preemptive design technique to shift the dominant costs of resiliency to design-time. In particular, union-free hypergraphs are exploited to partition the reconfigurable resources pool into highly separable subsets of resources, each of which can be utilized by the same synthesized application netlist. The diverse implementations provide reconfiguration-based resilience throughout the system lifetime while avoiding the significant overheads associated with runtime placement and routing phases. Two novel scalable algorithms to construct union-free hypergraphs are proposed and described. Evaluation on a Motion-JPEG image compression core using a Xilinx 7-series-based FPGA hardware platform demonstrates a statistically significant increase in fault tolerance and area efficiency when using proposed work compared to commonly-used modular redundancy approaches.