That support response seems consistent with the current Help Center article for API Organization Verification: failed verification attempts currently do not support retries, and manual document review outside the verification system is not available.
Also this same issue has been solved by @OpenAI_Support in this topic:Requesting Staff Assistance: Identity verification rejected - photographed ID on screen instead of physical ID (Pro plan, need API access).
And I understand that you don’t want create a new organization or a new account (if needed) but as I understand it, it seems to be the only workaround for retry.