Right now what the US should be doing is a full court diplomatic press on the government of Sri Lanka to close the deal. To be the bigger man. To be a Lincoln /Grant and recognize that one must be a gracious in victory as they are determined in battle.
Unfortunately I think the U.S. has little leverage over Sri Lanka at the moment, which is probably much more interested in embracing the PRC, especially given the Rajapaksa brothers' personal interest such relations. The Sri Lankan media is naturally full of denunciations of the West in general for seeking to investigate human rights violations and hinder military action, which in their view did nothing but protect the Tigers.

... and how do you tell the difference between a civil war and an insurgency, and why does it matter?
We could spend many posts arguing over the semantics of those two words. But I agree with Bob that the Tigers made a premature transition towards establishment of a mini-state rather than remaining a mobile guerrilla-based movement. The Tigers created an infrastructure and a government base that then had to be defended in conventional battle. They invested so much into their mini-state that they could not survive its destruction at the hands of a conventional army.

Most of the failure can be laid at the feet of the Tiger leadership. They irretrievably alienated India in the 1980s through their inability to accept competing Tamil nationalist groups. The assassination of Rajiv Gandhi eliminated any possibility that India would ever support a Tiger-dominated Tamil homeland, and only with Indian support could a Tamil autonomous region in Sri Lanka hope to survive in the face of determined Sri Lankan opposition.