One interesting issue I failed to include in previous discussions comes from Barry Bickmore's works on early Christianity. On a page entitled "The Angel of God's Presence in Abraham 1:15-16" (archived), Bickmore observes that the "angel of the Lord's presence" who rescues Abraham on the altar is also identified as Jehovah, and this correlation between Jehovah and an angel makes good sense in light of ancient Jewish beliefs but would be at odds with what Joseph would likely have learned in his environment. Bickmore, after drawing in part upon Margaret Barker'a The Great Angel, concludes:
We have established that Abraham's identification of Yahweh with "the angel of his presence" was consistent with the earliest Israelite traditions, and also with the earliest Christian traditions. But if we assume, as the critics of the Book of Abraham do, that Joseph Smith created this remarkable document by applying his fertile imagination to the sources he had at hand, how did he come up with this strange designation for Yahweh? The only Biblical source for the phrase would have been Isaiah 63:9, but we have seen that this verse gives no hint that Yahweh was equated with "the angel of his presence". This conclusion can only be drawn when the Greek text is compared with the Hebrew. However, the Septuagint was not translated into English until 1851, so again we are at a loss to find a source for the Prophet. Consider also that we have not been able to find even a single case where Joseph Smith used this title to refer to Yahweh, aside from this solitary passage in the Book of Abraham. Therefore, we are forced to conclude that Joseph Smith was inconceivably lucky in his choice of words, or in fact the Patriarch Abraham chose these words to describe his God.There are so many intriguing "direct hits" or "bulls eyes" that we find in the Book of Abraham that it would seem unwise to dismiss the book as a mere fraud. Something noteworthy is going on. Indeed, the strengths of the Book of Abraham could soon be more frequently discussed and appreciated, rather than merely discarding the book as a fraud as too many are too quick to do.
Update, Dec. 30, 2016: With helpful input from readers here, I've recognized that it is possible that Joseph could have picked up the concept of equating the angel with Jehovah based on biblical commentary. In fact, through searching commentaries at BlueLetterBible.org, I found that Matthew Henry's eighteenth-century commentary on Isaiah 63 specifically opines that the "angel of the Lord's presence" in Isaiah 63:9 could be Jesus Christ in the role of Jehovah. Henry states:
The person employed in their salvation-the angel of his face, or presence. Some understand it of a created angel. The highest angel in heaven, even the angel of his presence, that attends next the throne of his glory, is not thought too great, too good, to be sent on this errand. Thus the little ones' angels are said to be those that always behold the face of our Father, Mt. 18:10. But this is rather to be understood of Jesus Christ, the eternal Word, that angel of whom God spoke to Moses (Ex. 23:20, 21), whose voice Israel was to obey. He is called Jehovah, Ex. 13:21; 14:21, 24. He is the angel of the covenant, God's messenger to the world, Mal. 3:1. He is the angel of God's face, for he is the express image of his person; and the glory of God shines in the face of Christ. He that was to work out the eternal salvation, as an earnest of that, wrought out the temporal salvations that were typical of it.So I'll grant that there is a basis for commentary from others to have guided Joseph Smith on this point.