Universities are producing AI principles and use policies faster than they are building decision pathways for unfamiliar forms of AI agency. This study develops Institutional AI Governance Stress Testing (IAGST), a prospective documentary method for locating where publicly documented governance ceases to yield an accountable response. IAGST adapts established policy stress-testing and wind-tunneling logic. Its originality lies in combining controlled capability escalation, a frozen documentary corpus, a six-dimensional governance response chain, non-compensatory decision rules, and case-level breakpoint diagnosis. The method was demonstrated using 133 substantive public documents from five Western Australian universities and 15 quality-screened scenarios, resulting in 75 university-scenario encounters. Six cases were resolved, 14 were resolved through structured discretion, and 55 were indeterminate. Governed pathways fell from 16 of 25 augmentation cases to four delegation cases and none at autonomous substitution. The dominant weakness was not the complete absence of responsible roles: all 50 authority-gap cases named a role at only a generic level but lacked sufficient decision criteria or process. The findings show how universities can move beyond policy inventories and principal statements by testing whether authority, procedures, safeguards, and reviews remain connected as AI capabilities evolve. IAGST is a reproducible diagnostic for policy learning, not a ranking or measure of implementation.

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