Zero-Knowledge Proofs (ZKPs) have emerged as a powerful tool for secure and privacy-preserving computation. ZKPs enable one party to convince another of a statement's validity without revealing anything else. This capability has profound implications in many domains, including machine learning, blockchain, image authentication, and electronic voting. Despite their potential, ZKPs have seen limited deployment because of their exceptionally high computational overhead, which manifests primarily during proof generation. To mitigate these overheads, a (growing) body of researchers has proposed hardware accelerators and GPU implementations of both kernels and complete protocols. Prior art spans a wide variety of ZKP schemes that vary significantly in computational overhead, proof size, verifier cost, protocol setup, and trust. The latest and widely used ZKP protocols are intentionally designed to balance these trade-offs. One particular challenge in modern ZKP systems is supporting complex, high-degree gates using the SumCheck protocol. We address this challenge with a novel programmable accelerator to efficiently handle arbitrary custom gates via SumCheck. Our accelerator achieves upwards of $1000\times$ geomean speedup over CPU-based SumChecks across a range of gate types. We include this unit in zkPHIRE, a programmable, full-system accelerator that accelerates the HyperPlonk protocol. zkPHIRE achieves $1486\times$ geomean speedup over CPU and $11.87\times$ geomean speedup over the state-of-the-art at iso-area. Together, these results demonstrate compelling performance while scaling to large problem sizes (upwards of $2^{30}$ constraints) and maintaining small proof sizes ($4-5$ KB).