So, you have a non stamped vessel ostensibly being built to Div 1 (though not Div 1) with a reference to UT in Div 2 (though not Div 2) and your asking if its acceptable.
Considering your spec is all over the place (and no place) and its who cares to ASME (since its not ASME) I'd say if the client says its acceptable its acceptable.
If there is a technical issue with the method then the code references are a distraction.