Sounds like rock weed - floats because of the air capsules. Normally grows on rocks, buts gets torn loose in storms and goes adrift. Good stuff for a clam bake!
No suggestions on keeping it out of your cooling system. Perhaps a larger size thru hull & hose would allow it to pass to the strainer where it is easily dealt with. Personally, I don't like the outside strainers - no way to clean them without going overboard. Perhaps feed the head flush from downstream of the engine strainer?