An 8110-3 is signed by a DER. Not an AMT. It is a statement of compliance, not a statement of conformity.
AMTs are responsible for conformity to approved data and typically sign 337 forms. DERs are responsible for compliance to airworthiness standards and sign 8110-3 forms. We have similar forms in Canada (Mod reporting form and AE-100)
By the way....there is no way in hell that a 4x5 foot hole in a pressure vessel that isn't covered in the SRM is a "minor" modification or repair. Not only that, but the tech doing a such a repair needs a special rating. In Canada the limit is for holes over 6 inches.
Am I missing something in your explaination Blacksheep?