I guess the answer lies more on the opinion of Hesiod when he mentions the name Iapetus, unless you find that same "title" from other writers. Remember his writings are poems. Perhaps when reading them in Greek the verses in question sound more "profound" when the adjective "great" is added to the name Iapetus because his relation with human existence.
Like to say, in society there are several kind of leaders, but the part of the community dedicated to help homeless people will call "great" to one of their main sponsors, while such adjective might won't be used by them when is in reference to sponsors of school organizations and similar.
The honor to Iapetus given by Hesiod must be found as well from other writers of those times in order to catalogue it as the formal title. Find another "witness" calling him "great Iapetus" and surely will be a good base to research about it.
Sadly, little is known of the poets and their works.
It seems that Homer may have been a contemporary of Hesiod. Consensus view would have Homer about a generation older than Hesiod, though some scholars believe Hesiod predated Homer. However that may be, both seem to have been predated by Orpheus and (his son?) Musaeus.
Little is known of them and none of their works seem to have survived.
One thing that we do seem to know is that the poets Homer and Hesiod composed in the same style, and tailored their oratory to different audiences. In works and days, Hesiod claimed to have won a poetry competition, and even though he did not mention Homer, his claim of victory hinged on his focusing on the home and agriculture, while the loser focused on war and death.
What we do know is that Homer mentioned Iapetus, stating only that Iapetus dwelt in Tartarus.
The best we have is fragments of fragments and snippets of fragments.
So we are left with a single source for "Great Iapetus"
ergo, the question: "Why great"?
Even though my guess is fairly well informed:
Your guess may have as much merit as mine.
