Word order: "dear my lord" in Shakespeare

I'm revisiting my old question [#167151]. The original question was about the word order: “dear my love” or “my dear love”. I hold a position that we say “my dear love”.

But when I was saying a prayer yesterday, I heard myself say “dear my lord”, and it just sounded smooth to my ear. I looked up the phrase and I found it in Hamlet by Shakespeare. That made me think, what was in my mind when I asked the former question.

The linked site above for Hamlet lists line-by-line translations into modern English and the page shows the following dialogue in Act 3, Scene 2, Page 2:

[Shakespeare] CLAUDIUS: Thanks, dear my lord.

[Translation] CLAUDIUS: Thanks, my dear lord.

And my question here is not about which order is correct. Instead I wonder: If the word order was turned the other way around, when did the change occur, and why did it happen?

Answer

In general, the form appears to always have been "my dear X". It is now (unless you're writing a letter), and it was before Shakespeare's time. This can be seen in examples from Middle English, from this entry in the Middle English Dictionary (emphasis added):

And dele A-mong my Frendes · and my deore children.
_{The vision of William concerning Piers the Plowman (c1390)}

Luke it be done and delte to my dere pople
_{Morte Arthur (c1440)}

My dere sonne, I ȝef vp my sowle ynto þi hondes
_{Mirk's Festial (a1500)}

There are also examples of "my dear X" in Shakespeare's works, as can be seen here. So why "dear my X"? Hot Licks suggests that we "[c]onsider that "m'lord" is a title". I did find some evidence that "dear my lord/lady" was used by others, e.g. here and here (but neither of these are particularly close to Shakespeare's time).

However, the bigger problem with this theory is that Shakespeare uses "dear my X" when "my X" is not a title (e.g. "dear my brother"), as you can see here. Looking into this, I found a possible explanation:

Shakespeare occasionally uses a peculiar idiomatic phraseology similar to that employed in the Italian language. He sometimes thus transposes the adjective and the pronoun in a phrase.
_{The Shakespeare Key}

The book gives many examples of this, including "dear my brother", "dear my lord", "gentle my lord", and "good my glass".