Galium,
Stanford in the Vale did lie in the Archdeaconry of Berkshire, so, in theory, either the Archdeaconry of Berkshire or the Diocese of Salisbury could have been the issuing authority. In practice, one or the other may have been more commonly used at the time in question.
For indexes to the destroyed marriage bonds of the Archdeaconry, I think the most important repository would be the Berkshire Record Office. You could ask them if they would do a short search for you.