So........how or SHOULD hermeneutics change between dispensations or covenants?
Great question.
Hermeneutics is primarily an issue of literary genre, and only indirectly an issue of theology. Literary genre relates to the occasion for the text -- its rhetorical purpose, its historical and social context -- but the main issue of concern is, How are words and phrases used by that text? Once we have defined our text, we use the different places the phrase is used within it to understand what that phrase means. This process is typically automatic, except in the academic world when it forcibly becomes methodical and the reader reflects more on how and why he or she is reading in a certain manner.
Of course, before any of this happens, the limits of the text must be defined. This relates directly to your question.
Now, "text" can be taken as narrowly or as broadly as the reader wants. Your "text" could be the Christian worldview, the Christian canon, the Bible, the Old Testament, the book of Genesis, or the myth of the Nephilim. Depending on what you see as your text, the con-text is going to affect your interpretation differently.
The concept of a "dispensation" is not one that I find particularly useful, but with the concept of a "covenant" we see two "texts," one before the resurrection and one after it -- loosely speaking, the Old Testament and the New Testament.
Now, how does this relate to the idea of the "son of God"? I would suggest that before the incarnation the term is meant in terms of
resemblance,and that's all it could mean. However, the first advent of Christ brings forward a number of new, more concrete meanings -- not resemblance so much as
nature. Clearly our understanding of the phrase "son of God" must change from Old to New Testament.
This reading is bound up in a
covenantal hermeneutic and if we choose to define our text differently we will end up with different results.