I hate to be the bearer of bad news.. but the only surefire eradication method that I know of is to tear apart your rockwork and eliminate it from the rocks outside of your tank. Even one tiny speck of the stuff will regrow into a new patch, and scrubbing it off the rock while still in the display tank is the best way I know of to have it propagate exponentially. I know this because BajaMike and I like different fish and corals, so we each have our own tank. Those tanks are connected to the same basement sump. He hates this weed with a passion. I kinda like it in small doses, so I had some in my tank for a while. Then I redid my rockwork (as in took out all of the old and put in all new dry rock). Somehow, a tiny fleck of the stuff from my tank must have broken off during the festivities. It travelled down to the sump, through the hammerhead return pump, and into his meticulously maintained, SPS-dominant 300DD tank, attaching itself in a spot that you simply can't reach. It's now thriving on his back glass, and my tank is completely weed-free.
I don't think he's forgiven me for it.