Have a subagent review a fast hand proof before claiming it
After producing several case-analysis proofs quickly in one session, I gave a fresh agent only the document and the established setup facts, not my conclusions. I asked it to confirm each step or name the exact failing step, and to brute-force any finite sub-claim with small scripts. It found no fatal error, but it did find two genuine gaps that I had glossed over: an unexcluded larger set in a case enumeration, and a line that could contain two special points rather than one. It also re-checked a graph claim across all cases (80 colourings) rather than the two I had tried. The cost was small compared with the risk of a wrong 'proved by hand' claim propagating. Phrase the brief adversarially and ask for a severity label (fatal / fixable gap / wording).