Telecom-band spin defects in silicon offer a compelling platform for integrated quantum networks by combining scalable silicon photonics with spin-based quantum memories and multiqubit registers. The T center and recently demonstrated Al1 center are particularly promising, but their limited coherent zero-phonon emission requires strong cavity enhancement for efficient spin-photon interfaces. Here, we inverse-design silicon nanobeam cavities for both centers using a unified adjoint-optimization framework targeting Purcell enhancement, resonance alignment, and photon extraction. For each emitter, symmetric cavities maximize Purcell enhancement, while asymmetric cavities provide directional coupling to an integrated waveguide. Three-dimensional finite-difference time-domain simulations yield loaded quality factors up to 3.25 x 10^6, Purcell factors up to 1.43 x 10^5, and cooperativities of approximately 280-5000, corresponding to cavity-coupled emission fractions exceeding 99.6%. The asymmetric cavities direct approximately 90% of emitted power into a single on-chip waveguide while maintaining cooperativity above 280. Under nanometer-scale fabrication perturbations, all four designs remain within the high-cooperativity regime, and high cooperativity persists when the cavity quality factor is constrained to a realistic absorption-limited value of 10^5. This unified, fabrication-compatible framework establishes a scalable cavity-design route for silicon telecom spin-photon interfaces and, to our knowledge, the first cavity designs for the Al1 center.