First off ya have to know there is no evidence that Joseph had an 1769 copy of the Bible in his possession, that puts a big kink in the argument.
Okay there is a flimsy answer to this; we don't have this original part of the manuscript of the Book of Mormon. It could be Oliver as he prepared the printers copy goofed and added in the word Red.
However that does not explain the other change the Book of Mormon makes.
KJV 1769 "....and afterward did more grievously afflict
her by the way of the sea, beyond Jordan, in Galilee of the nations."
BoM "and afterwards did more grievously afflict by the way of the Red Sea beyond Jordan in Galilee of the nations."
The word 'her' is missing while the word Red is added??
Now this is what the antis don't tell you, the Masoretic Hebrew text from which the KJV came from
does not contain the word 'her'.
"...and in the latter time he will cause the way of the sea to be honored, the other side of the Jordan, Galilee of the nations." (neither is it in the Septuagint)
So this small seemingly unimportant change by Joseph matches the original more precisely than the KJV does. And I just bet he didn't have a Masoretic Hebrew text sitting in front of him.
Reading through this it really makes one wonder what the original intent was.
*In theory what you find in the Book of Mormon is the closest to the original writings of Isaiah.
Let's but this in context;
1 Nevertheless the dimness shall not be such as was in her vexation, when at the first he lightly afflicted the land of Zebulun and the land of Naphtali, and afterward did more grievously afflict her
by the way of the sea, beyond Jordan, in Galilee of the nations.
2 The people that walked in darkness have seen a great light: they that dwell in the land of the shadow of death, upon them hath the light shined.
6 For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace.
So it is about the coming of Christ. The words 'by the way of the sea' is referring to what was an old high way.
The following is written by D. Charles Pyle and I found it at FairMormon;
"....On the other hand, it also is possible that it is not an error at all.
The King's Highway also was part of what was known in ancient times as the Way of the Red Sea, which led out of Egypt along the shores of the Red Sea, passed through Edom and changed direction after meeting with the Way of the Sea, in Galilee, to go into Mesopotamia. It is possible that Joseph journeyed this way, or at least part of this way, to avoid going through Judaea when he took Jesus into Nazareth as a young child. If so, it would be quite correct in that the light would pass into the region of Naphtali via the Way of the Red Sea. Joseph sought to avoid contact with Archelaus and a back route would be one of the best ways to avoid contact."
So it is possible and even likely the Book of Mormon is the most correct!
See a map here;
King's Highway (ancient) - Wikipedia