On the question of "what's the best way to eliminate them?" This is always a tough one. In examples around the world, biologists have introduced natural predators to control the population of a non-native species, often times only to upset the environmental balance in a different way. Fortunately they don't have to do that here, as the grouper could probably keep them under control, if only their numbers were larger! Let's hope that some of the marine reserves will help their population. Hunting is probably the next best hope, but unfortunately lion fish can go much deeper than recreational spearfishermen or scuba divers. Doing tech dives just to hunt lion fish probably isn't going to get many takers, so the lion fish have a safe haven by staying deep.
Too bad you can't trap 'em like we do everything else... bears, rats, mice, etc!
On the question of "Should they be eliminated?" I say absolutely. We as humans made a mistake by introducing them into the non-native environment, that mistake is going to have a massive impact, we should absolutely try to correct that mistake if possible.