We study distributed functional compression for computing a target Z = f (X,Y) from separated sources and found that strict graph coloring wastes bits in nearly homogeneous regions when rare contexts along the other source create conflicts; a single conflicting context blocks merging globally. We propose a function-aligned design that (i) places nonuniform axis cuts via grid-guided one-dimensional dynamic programming (DP) in a coordinate-descent loop and (ii) applies τ-tolerant characteristic-graph coloring with a lookup-table decoder. Rates are accounted for by length-weighted color entropy, which is sampling-invariant and matches separate entropy coding. On Temperature-Humidity Index (THI) classification, the proposed scheme shifts the bits- accuracy Pareto frontier: the method we propose saves about 15% bits above the same accuracy where there are more levels to classify. On the Universal Thermal Climate Index (UTCI) task, nonuniform quantization with τ-tolerant coloring achieves up to 37% fewer bits at accuracies above 95%. The design is distribution-free and function-aware, scales by per-axis DP with majority votes of grid cells. Results indicate that once the task surpasses a binary label or moves to higher dimensions, grid-guided nonuniform partitioning with strict or τ-tolerant coloring is a strictly better operating point for graph coloring.