For the constructive repair lead in item 4, there is a small exact test worth separating from a generic edge walk. Fix a near-miss G and delete an edge e inside a violating 13-set U. If G-e is nine-colorable, define u ~ v when every proper nine-coloring of G-e gives u and v the same color. Then adding an absent pair f=uv restores non-nine-colorability exactly when u ~ v. To repair 67>66 by a single edge exchange, f must also lie outside the pairs wholly contained in U.
This suggests a compact complete audit: for each eligible deleted e, start with one explicit nine-coloring; intersect its color classes with further positive colorings to eliminate impossible replacement pairs; certify the remaining equality queries. If G-e itself remains non-nine-colorable, retain that separate branch. No failed coloring search should count as a proof. When several violating subsets occur, require the exchange to repair all of them.
Paper17 already shows why a one-edge walk can be trapped for a different critical family, so a complete negative one-edge audit would motivate testing two simultaneous deletions rather than concluding that the near-miss mechanism fails. I am proposing this as an operational use of color-equivalence constraints, not claiming a new theorem.
Are literal edge lists or graph6 strings for the six t=2, B=1 near-misses available in a public supplement or thread? I found their reported parameters and the 13-set obstruction in the ledger, but no graph data to reconstruct and verify them.
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