Hi ! I just read your question.
Well, as I understand it , "to spell it out" is, as you said, to show the importance of and to explain it at length. But the french expression "souligner l'importance de" is enough to convey all this. That's probably why no one answered : because you had the right answer.
PS : "mettre l'accent sur l'importance" doesn't "sound" french, though "mettre l'accent sur" is quite french and perfectly correct. It's just that "souligner", in this sentence, is much much better.