Defunct websites are near impossible to go back to, but the University of Denmark has has some acclaimed success in dating these old manuscripts. The dead sea scrolls date from 200BC, which does not negate Isaiah being finished in the 350 range. Who could have written them? Isaiah could have started them, and they were finished as new theology came into play. Or someone knowledgeable in Jewish history may have written the entirety in his name. Just as an aside, not all of Judaism had a favorable view of Isaiah, as he was considered a false prophet by the Deuteronomy test; however each of the popular prophets had their own "fan club" who would have sought to defend them.
I have never studied the deutro isaiah theory, but here is someone who has:
"Isaiah, Deutero. Isaiah includes amazingly specific prophecies that came true centuries later with exact accuracy. The apologetic value of this prophecy, however, has been blunted by the critic’s charge that there were at least two Isaiahs. They claim that the second, later Isaiah records history, rather than sets out predictive prophecy.
The traditional view of the book of Isaiah is that it was written by Isaiah, son of Amoz, between 739 and 681 b.c. However, negative critics argue that “Proto-Isaiah” encompasses chapters 1 through 39, while Deutero-Isaiah wrote chapters 40 to 66 in the fifth century b.c. If so, then the amazing prediction by Isaiah including the one that a king named Cyrus (Isa. 45:1) would be raised up by God to discipline Israel loses its prophetic punch. For if one and the same Isaiah did not write this some 150 years before Cyrus was born, but after he had lived, then there is nothing amazing about knowing his name.
A Response to the Hypothesis. The traditional view that the book of Isaiah is a single work written by the prophet Isaiah is supported by several arguments.
The critical view that separates Isaiah into two or more books is based on the assumption that there is no such thing as predictive prophecy. Modern scholars claim that the prophecies in chapters 40–55 concerning Cyrus must have been written after Cyrus ruled in Persia. This view is antisupernatural and tries to explain these sections of Isaiah as history. However, since God knows the end from the beginning (Isa. 46:10), it is not necessary to deny the supernatural element in Isaiah’s prophecies (see Miracles, Arguments Against).
Differences between the two halves of the book can be explained in ways other than the two-author approach. Chapters 1 through 39 prepare the reader for the prophecies contained in chapters 40 through 66. Without these preparatory chapters, the last section of the book would make little sense. Chapters 1 through 35 warn of the Assyrian menace that threatens to destroy God’s people. Chapters 36–39 form a transition from the previous section to chapters 40–66, by looking forward to the invasion of Sennacherib (chaps. 36–37), and at the spiritual decline that is causing the downfall of Jerusalem (chaps. 38–39). These four intervening chapters (36–39) are not in chronological order because the author is using them to prepare the reader for what is to follow.
The difference in words and style of writing between the two sections of the book has been used by critical scholars to substantiate their claim that there are at least two different books. However, these differences are not as great as has been claimed, and the differences that do exist can be explained as a difference in subject matter and emphasis. No author writes in exactly the same style using precisely the same vocabulary when writing about different subject matter. Nevertheless, a number of phrases found in both sections attest to the unity of the book. For example, the title “the Holy one of Israel” is found twelve times in chapters 1 through 39 and fourteen times in 40 through 66.
Similar Phraseology in the Two Parts of Isaiah
Chapters 1–39
Chapters 40–66
1:15b—“Your hands are full of blood.”
59:3a—“For your hands are defiled with blood.”
28:5—“In that day the Lord Almighty will be a glorious crown, a beautiful wreath for the remnant of his people.”
62:3—“You will be a crown of splendor in the Lord’s hand, a royal diadem in the hand of your God.”
35:6b—“Water will gush forth in the wilderness and streams in the desert.”
41:18—“I will make rivers flow on barren heights, and springs within the valleys. I will turn the desert into pools of water, and the parched ground into springs.”
In Luke 4:17 Jesus rose to read in the synagogue and “was handed the book of the prophet Isaiah.” The people in the synagogue and Jesus himself assumed that this book was from the prophet Isaiah. Other New Testament writers accepted Isaiah as the author of the entire book. John 12:38 states that Isaiah was the one who made the statement that is found in Isaiah 6:1f. and 53:1. Other instances where the New Testament ascribes portions of chapters 40–66 to Isaiah include Matthew 3:3; Mark 1:2–3, and John 1:23 (Isa. 40:3); Matthew 12:17–21 (Isa. 42:1–4); Acts 8:32–33 (Isa. 53:7–8); and Romans 10:16 (Isa. 53:1).
The Dead Sea Scrolls include the earliest complete copy of the book of Isaiah, and there is no gap in the scroll between chapters 39 and 40. This indicates that the Qumran community accepted the prophecy of Isaiah as a seamless book in the second century b.c. The Greek version of the Hebrew Bible, which dates from the second century b.c., treats the book of Isaiah as a single book by a single author, Isaiah the prophet.
Even if the critic could show that part or all of Isaiah was written in the fifth century or later, it would not disprove the supernatural nature of the predictions about Christ. Those were fulfilled centuries later than even the latest possible date for its appearance. Isaiah predicted the virgin birth of the Messiah (Isa. 7:14), his ministry (Isaiah 11; 61), and his death for our sins (Isaiah 53; see Christ, Death of). Isaiah 53 is so specific and so messianic that even rabbinical interpretation of it before the time of Christ viewed it as a prediction about the coming Messiah (see Driver). Indeed, even if the writing is dated to the late fifth century b.c., it is a clear and specific supernatural prediction about Christ given hundreds of years in advance. If Isaiah had a supernatural source for this prophecy, then there is no reason to believe he did not have the same supernatural source for his predictions about Cyrus.
Conclusion. The attempt by Bible critics to posit a second and later Isaiah does not negate the supernatural nature of his specific predictions. They do not even succeed in proving that there was a later Isaiah who wrote 40–66. Hence, Isaiah’s predictions which mention Cyrus by name over 150 years before he was born still stand. Even were Isaiah dated later in part or in whole, the book is filled with specific predictions, especially those literally fulfilled by Christ that were made centuries in advance.
Sources
O. T. Allis, The Old Testament: Its Claims and Its Critics
———, The Unity of Isaiah
G. L. Archer, Jr., A Survey of Old Testament Introduction
S. R. Driver, et al., trans., The Fifty-Third Chapter of Isaiah According to Jewish Interpreters
N. L. Geisler and T. Howe, When Critics Ask
R. K. Harrison, Introduction to the Old Testament"
Geisler, Norman L.: Baker Encyclopedia of Christian Apologetics. Grand Rapids, Mich. : Baker Books, 1999 (Baker Reference Library), S. 367