I have mangroves but it's more of a novelty than anything else.
I'm sure they pull down NO3 but they grow so slowly that they can't really be relied on as a means for nutrient export. You'd need .... well ... a lot. Easily a mangrove or two per gallon or more. There's actually some rule-of-thumb but I have no idea what it really is.
There are other macro algaes that can be used as an alternative to the prone-to-sporulation caulerpas and halimedas. If you can get ahold of some
Chaetomorpha linum "spaghetti algae" that stuff works well but needs bright light to grow quick enough to be effective.. There's also another kind of algae that works well but I forget what it's called now.
Something like "shaving brush" or something like that. Hmmm, sorry I can't remember what it is now.
I suppose, though that any kind of algae is going to be problematic in a high-flow area though. I'd maybe look into a lower-flow kind of refugium or hang-on-back type arrangement or something like that.