all invasive macroalgae are highly susceptible to in tank peroxide use and none of the other animals you listed are. This is a viable option. if you would like to see endless examples of before and after pics its in our thread in the nanos forum, pico reef pest algae problem challenge. I know you asked for natural methods, if those don't work this will. the current tanks we are treating on the last pages are 400+gallons and 200+ gallons
the actual sargassum cures are linked out to 3reef its not actually in that thread, but enough comparable kills of fellow invasive macros are, and sargassum responds the same, its highly susceptible, among the easiest things to kill with it.
B