Reconfigurable integrated photonic spectrometers can generate exponentially increasing measurement states from a small number of switching elements, making them a promising design class for high-performance portable spectroscopy. However, selecting a circuit architecture remains largely intuition driven. We introduce a grammar-based topology optimization framework that composes standard photonic building blocks, canonicalizes and physically prunes candidate circuits, and jointly searches topology and component parameters using a coherent scattering-matrix model. Designs are screened by a decoder-independent architecture objective that combines absolute singular-value noise gain with multi-line conditioning, thereby accounting for response diversity and optical throughput. Direct held-out spectrum reconstruction confirms that this surrogate is a strong predictor of reconstruction quality at high incident signal-to-noise ratio (SNR). Across the nonresonant and resonator-augmented design spaces examined, dFT and its variants offer the best balanced performance; increased component loss favors a shallower dFT variant in which one differential-delay stage is replaced by an analog optical phase shifter. Passive and active rings provide no robust advantage attributable to resonant amplitude coding. The results identify balanced complementary interferometric responses, efficient terminal collection, and limited lossy circuit depth as central design rules, and establish a systematic route for selecting task-optimized photonic circuit topologies under technology-specific constraints.