We have here a hymn of a known author, Bishop Heber, who wrote a known set of words, published in 1811. There is no reason to suggest that he "really" meant what he didn't publish - ie "suns" rather than "sons".
The writer is clearly addressing the Star of Bethlehem, and praying that today's (ie his contemporaries) Christians will be led to Jesus, as the magi were led to his cradle, by following the Light (Jesus and His message.) There is a whole set of theological arguments to do with Jesus Christ as light bringer - most of St John's Gospel for a start!
"Son of the morning" = "Morning star" = "Bringer of the Dawn". He brings light to the world, as well as the individual soul, and the darkness fails.
I have no argument as to tunes - I only know one - "Epiphany Hymn", but I'm certain that there are many others, just as good, if not better, both in tune and arrangement.

Chris B.