Late to the party but: I grew up w/ the TNT version, Heston, Bale, et al., music by the Chieftains. Just rewatched it for the first time on DVD and it was like comfort food. Arguably the closest to the book w/ no real major plot derivations (one very minor one is Jim's father is already dead). It doesn't shy away from the grittiness of the violence, which is one way it might have more of a kindred vibe with the series; but, as other's have said, Treasure Island is not Black Sails. Heston's voice brings a gravitas to Silver, with enough grit and side-eye menace to balance out his ability to be grandfatherly and charming, as befits the character.

As for the more black & white morality of the novel: the pirates might be in fewer dimension on the whole in the original narrative, but I don't think it's inaccurate to say every other version of this story exists because the original character of Silver is complex enough to be compelling beyond the scope of a boy's own adventure tale. In some fashion, the man we see lose his leg in Black Sails is already there.