Fluxonium qubits demonstrate exceptional potential for quantum processing; yet, realizing scalable architectures using them remains challenging. Here, we propose a scalable fluxonium-based square-grid design with ~63 ns controlled-Z (CZ) gates, achieving coherent errors below 10^{-4}, activated via microwave-driven transmon couplers. Furthermore, the architecture natively supports ~70 ns CZZ gates – three-qubit operations composed of two CZ gates sharing a common qubit – which directly implement two-qubit parity checks central to quantum error-correction protocols and reduce the incoherent error by ~35% compared to sequential CZs. A central difficulty in building large-scale systems with all-microwave gates and, therefore, static couplings, is suppressing parasitic interactions that extend beyond nearest neighbors to include next-nearest elements. We address this challenge by introducing several design strategies, including frequency allocation for both qubits and couplers, localization of coupler wavefunctions, and a differential oscillator that suppresses residual long-range interactions. Together, these principles establish an interaction-resilient platform for large-scale fluxonium processors and can be adapted to a wide range of fluxonium layouts.